geometriya 10 klas burda by zimzone1

NOBTOPEHH9 KYPCY NIAHIMETPIi

y roAi6srx

rpsRyrrtnrciB BiAHoueHns BiAroBinrqx cropiq piBEi i AopiBErororb oeOiqi€Ery roAi6gocri A. y rrEoMy saeAaEEi e sopissro€ siasoue";; *""",""

MeroA AoroMi crrn! rpxrcyrEnrciB: 1) Bi{mynarn rra Marrrorlny a6o Ao6yAtBaar rpur{yrHrr{! eneMe}Irs.sKoro Morir-

3rlairn;

2) sKqo sllaiAerlrfi

eneMeEr

poBB'sayBaIII]i saxirlrrennfi

3) slirlo lri

rpr.rKyrriHKa

1' 1)

'=8

-i

ie30'=e

*,,=*=l'

+=r"6

r"*);

a,: b, + c, _ " Hacairor: ' eosa= ''2b. Tcopeua c,{HyciB:

,=C,.rt=H=+-g,6

^d10 o, r

(cu);

x=nE +"" mc*"a

- cos.r at+"' 3t =

6rc.

2:9 2=18(cMti 6 2=t2tcvl.

i=,

5e4pe'Jvit (AO

rporrnex{di croponr-i ra&o}ft. MOD DO) sI{ troroBnHn Aiaronaneit, ZOAD : IODA.

f!= ll3ArAr: q-aen 'aD12--

tCAD = : ti

3) re ZCAD =

24);

O,75i

-CAD

piBHo_

37".

o,5333i ZCAD

- 0.n,ur,

ZCAD = 23";

zn,

(prc. 26).

.v.

AiaroHa-ni npiMoriyrHsKa piBrd,

1pn". ZS1;

BiAnoqiAb: 18 cM i. 12 cM.

2bc cos tt.

.L = srnp .b ^ '!slnc' stnY

BiAnosiqb: 26 .M

paAivc onrcaHoro Kona.

;=.9!ll1 \ srnL=,L: stn Y smo Z1

l-9=f 4. 1h=d r,s 3=22tcMti2 J - 36(cM). a61 BiAno1iAb: 27 cM i 36 cI,. ,l 1^ t 2t k--;-;=; 2t 13.2 26(cvr: 15.2- 30(cM).

1"ny,

':00", "r',y=$=1' y::0..

TeopeMa RocnHyciB:

sa qboMy rpoqec

cos60d=8.i=, niI,, ,=r."r,1uo.=r.@=nrg

'=s

posB'.sstioM saAarri,

BrrrcopncraeMo sr{afiAeEi eneMeErr.r Ans posB'ssaaHs EacrynEoro r. A., nolrs Ee orplrMa€Mo po3!'.E3oR 3aAaqi.

€

2a".

.4iaroFani rapajrenorpaMa roqxoro neperz rly AirsrEcs EaBnir:

3 ACO, 3a reopeMoro IiocIrIIyciB:

oc=4. 2

OD=: 2

noAi6Eicrr, rprriyrEnKiB nodtoBj npuKUmhuEu rpr.rRlrHuKn. y er{r.r x cropoH oaHoro rpr.4r(yrH r,{a Mox{Ha oAepxarn i3 cropiE -Apyroro Mrior{eHrr.sM Ha oAEe ii Te caMe AoAa?$e qllcno. OBIIarcII

qo 4na xyrlr oAuoro rpsriyrHrxa BiAnoriAHo piBsi ABoM l{yraM nrllloro, ro rpnRyrssKI, noai6Hi. 2. flxqo 4d cropoHn rprrftyrllrina rponopqifiHi ABoM c,I.opolIaM iHrroro i Ilyrrr Mixr qr-rMr{ croposaMu piBIIi, ro rprr(yrHt Rn noAi6Hi. 3. flKqo rpx rropolru oAHoro rpr.rHyrsnRa nponopuiirsi rpboM BiArrosiAHxM ..ro poEaM iEDroro, ro rpuRyrEn&q roAi6rd. &oeQi\i€Hn noAi6Hocni qllcno &, piBHe siAnoIIIeHHro BiAxoBiAHrrx cropiH 1.

noAi6rrx rpll&yIHrrxiB.

3, 1) LABD - LCBD 3a AsoMa cropoEaMa i n:lIo\a r..-:..)F HnMu (AD : DC, BD crin6, Ha cropoEa, tBDA - ZBDC\. (p.dc. 27) 2) LABD : LDCA Ba cropoHolo i AoMa npsnernrrMs &yraMr (,4, crdnlHa cropo-

ICAD: ZBDA; IBAD: ZCAD tl:( cyMa piBHrjx xyriB) (pnc. 28). 3) MDE * LCDE sa apboMa croposaMr (.4t : EC, AD : DC, DE - ctrirltra c"oMlg, = ACE, 3a rpEoMa croposaMr. MBE - LCBE s apr,oMa cropo!'aME. (prc. 29) Ha,

732 ti:l rEoMErptr

6ypaa M. t., rapaceHKoBa H. A. il::l:lillli:iiltti:::rl:.:

^ACD

\"eo

BC = AD. B ABCD

6. 1) -4, =

,tt t a - z"a*.".

cos

10,

zBaD

- BC'+CD'z-BD' zBC. CD

L0 'o,94

oD = 1@;e - 6to n,s4 = 6tBD:2.2,14:4,2a. cosznco

=-2,]€,__!4a 2- 4,42.6

f5o

s6a = .[as -

os,a = a,

,'BD

,lE"

z,rt

_ 23.23 + 36 18,32 57,84

za-BD=LAO.-45"*135.. 2l AD = Bc = ,E; t2' - 2. 5.12 /Josw = 14os

rrz3 = +,az 1c.,r1. 1c*1.

- 0,71; -BCD

= .Eb + 144

1ro 4,u

45'.

+ ("I,Iy.

+6, s.rz.o,ez=u's,

ao_eo.o.ez =r.+1,

6.87 tcn).

r:iiii:i:::::.j:+:iii:i;::i;t::::::i

rEOMETptq 6ypaa M. t., TapaceHxoBa H. A,

:iif 733

_-l

"or,BCD

IABD = 1AO. 55. :125.. q on = Js" *2,s" -r.s-*zr

B, = 6,32

: BM + MC, AD : AN + ND, ao4:. BC:-4r:4 + 6 = 10 (cM). BC

25 6'87'- 7056+25-47 20 =a'4'2.a,4 .5 "0,s8, -BCD,5b.. 84 =

Bidno6idb:

Jr, +6,15 ,-"4,85 =,40=a,to (c.),

cM.

=.,ts" *

cepeAsEa EiApi3KiB,43 i CD, ArEa napa,ne,rorpaM. AD: 7 cM EK nporlr"rel*{fli cropoElt

7. Toe4aO

naparenorpaMa. 2) - ABC ,/ BAD 72'nx anstpruri cropoHni npr,4, BC i ci,:.*ifr AB,

.tryrf{$ka

P:2d + D. IleptrMerp troAi6Eoro

rpI,I_

P:2

12:48

3\ P = 2.25 + 14

(cM); h =

18 (cM);

a = !, 12 2

,123 '-a2'

64.(cM);

p'= 48 1= 24 rcur.

P' =

n=2fi=z; r'

rc.1= 27

aa. 2

1) Po3rnnHeMo ABOM i A,ON. B rlr,Ix BO : DO sK rono8r-lEr AialoHati

lHyrpi

LBOM

LDON 3a cropoEoro

AiaroEarei.

ABoMa

rrpaNli,

aep.tlia AB. K

niEiE.

Fna =

cepFat{Ha

Ar'

Aa. FK -.cpca-

:.4,8. 2

TalclIxt .{nEoM, cropona poM6a AoplBHloe nonoBrEi croposn rprl{yrHnxa.

P la /B=r=i=ti

ffi

{cM):

t AE - AB=3 cv, P"^.,. --' 3 4 2

rpnMa,

12 (.M).

BiAno'iAb: 12 clI.

Br,

l,i, IMBO :

BF : FC, ro6ro a

"ropo"' ticxi.nrxz Zr I AC, FK AB

ToAi EF - cepe4Hq,liHit. LF 'l tss

rpr-

nernxMu Kyra.qr. 3 piBHocri rpfiRyrHt KiB BsnnuDae piBHicrb eiAfloBiaErx cropis: O,,l1 = ON. UIo r; rpe6a 6yno AoBecr'.

2) y nep in.racrr.rEi sasaqi Mrr ,qoserr, slo BOM = A,O-M. AEano rrHo aoBonlrMo, qo LCOM : LAON (AO: OC, ZMCO = INAO, tMOC: INOA).BBiacr BllnnrBae, t\o MC = AN.

734 illi rEoMETPlg

AC A. ,BC piBrri, roai

voro od,rFcd B

Hi pisEocropoHHi nps rrapare,lbsux trpsMnx BC l AD i ci'qHj,n BD. t1!'

"K rIo Micrnrb nporlr,'le){llri croposr poM6a, ro 3a reope-

(cM).

ro.rEa fleperrEy iioro

P! = 4!.

2t P:18.M

12, ABCD laparenorpaM, O rlla rpoxoarrE qepes ro'r(y O.

: ZNDO

na.

cepeArHa EC.

9. 1) PscD:3 5+9 = 24(cM);

grr Beprtry'ant

ierr"

128 (cM).

ABCD piBEo6i'{Ea (,4-B : Cr). BC : a, AD : b. AiaroHanb AC 6iceftrplrca Ryaa l. ZCAD : ZBCA EE BryrpirrHi pi3nocropoEEi rrpv BC I AD i ci.rHin -4C. 'loai IBCA: IBAC, M-BC - piBlro6eapeEr{i, AB:BC:a.P^a."=3a+b.

IBOM : ZDON

porl6, BtrncaEr1ii y piBsocropoHEii rpxliyrABC, ZA cninbHrrii. '{v:{ lr AiaroHai6 A,E poM6a - 6i.etsrpx.a Rlra ,4. ToAi sa Bnacrn3icrlo 6icexrptcn Kyra rpllnyrHfirla Borra arnu r6 cropoHy Bc -a BinpirHM, nponopu'iiHi cropoHaM

ne (cM).

Tp^ne\i"

2\ PBCD:3. 8 + 4:28

A-8.

AEFR

14,

P' = kP, Ae h = 9.

P:2.18

cropo4a, ,IMAC : ZNCA tII!' r'y'tt npu ocFoR:t, AM : CN F K ro,toBnu,, prBxxx 6iqtsvx cropiH rprK'1. 'rHa M,,Ur AC \ 4 ra ABoMa cropoHsMr.i i KyroM MrlK RHvr. 3 piBHocri rp'nyrHu(tBt AN - MC.

a- 1\

flopih: aD

n, npoBeAeni 3 BepI[Ijn Ao ocHoBI'I. - l{eaia Po3MnHeMo rprrKyrsrreuAM. LCNA. AC ix cIlirt''ja 2) AN

pirro

IlepnMerp AaIIoro rplr&yrHslia AopiBEme

pisEo6e4peE i s ocEoBolo,4C. 13. M-BC ll Al: i -.D bi.pnrprrx KtrrB opr o.HoBi.

troBiAHr.ax

roAr ra o3Fakoo

rM.

Po.rrneHeMo LADC i LCEA. AC lx cnii6sa .ropo4a, ZDAC : ZECA Fr< wrt npn oc]doBi, IDCA: AEAC eH nonoBnHu pienH\ qyriB npu ocHosj. MDC = LCEA Ba cropoHoro i ABoMa trprnernrMr RyraMu. 3 pisEocri rprnyrHaniB B'rnnlIBa€ piBEicrr, Bi,q- .4

a' r s s.o,es -.rlt,s - z,zq kfi.

lD : lao" 2. 32' = 116" zc:14o.-116"-64".

1\ BC

: AD sK cyMI' piBllrr( BiApisxiB.

EypAa M, 1., TapaceHKoBa H. A. l:::i:::;;i:ii:i::iii:iiiiliil:1

I{yrn, Bn,rcarf B oAHe rv caMy ,qyry, piBHi.

Kono,

fni

cnspalorr'cn Ha

15.

3a-qa.ra otropEa.

LMAD

LMCB,60B Hxx J()1 it4.Ei,lhHxr.i.

Hyrr

npr BepurrHax I i D piBHi ra BnacflIBicrro

Bnu-

EoAi6Bocri rprxyrHutriB BL{nn Ba. nponopuis

MA MD-. MA MB

3Btncb

MA MB MC

\l D.

i:itlit:;il:llii;:ilti':'..::,:i} TEOMETPI9 EypAa M.

1., TapaceHKoBa H.

i::li

73s

16.

Sa,qaqa oropEa. Po3rnsneMo rprxyflrrKlr MAC i MBC. BoH,l Eoni6si. o.nirbRr, . M y Hr4x cEirbs fi, a ,/ MCB - ,/CAB.60 Ko)l(eu 3 Hr-rx BfiMiprocrbca nonoBr,rllolo ayrr-r BC. 3 ooAi6socr i TpHxyrHr.rxis Brn"reraae nponopqit

MA MC

IeoMerpnqEni ctroci6 Do6yAoBIi cepeas!'oro rponopqiiEoro aBox BiapisKiB: Heo6xinHo 1106!AyBarr Kono, rjaMerpoM sRoro c c)Ma 4oBr+${H laHHx Birpi3KiB, roAi trepnesarrynsp, rpoBeaesui 3 rorrRlr s'€asaEHn q,lx BiApisftiB Ao rleperlrsy 3 r.onoM, rnynaErri Eiapi3olc. A.4 BC .1ABC :90", sic Bm.rcallrii Kvr, qo cffr- npsuonyrHlrfi, pacT6.s Ea liaMerp. BH B^aora qbolo rpxxyrHIrKa. flfta va€ raxy snacTuBicrE:

20. 1) AincEo,

MB'

BHz=AH.EC-

sBj.nc]{ MA MB : MC'.

B[cora npsMoxyrrioro rprKyrsar(a, npoBeaerra s BepIIIlrEll Ilprrrerrloro &yra sa rifioreEysy, aopiBHro€ cepeAHr,oMy fipofopqifiHoMy npoenqiii riereriB sa rinoTesysy. 17-

ABCD

rpaneqis, BC ll-4n.

}jexeir ZA + ZD - 9O". Ilo3,Ia.{l,,*ro ZA = d, 'rol':. ZD : 90" - a. fipoBeAeMo 8X I CD. Toni ZBKA : tCDA :

2I. 1)

:90'

Ct (BiAroBiAni Ilyrn rpr rapanenbsrrx FD npfMlrx BK i C, i ciqllin AD). V MBK zB:180" (1A+ Zt{'J:180" (Ct + 90" s): 180" - 90":90". TaRnM .rnHoM, AAB-K fil."rJqo BE L AK - npnMoriyrHnfi. - Bttcora MBK, ro All i E-K BiAnosiAEo rpoeKqii nareriB AB i B-K Ha rinoreEFy -4{. Bt' : AE EK.

A-re

iil

::;

i:i i:j rii .:1.:.:t :.f!r-.:

.Er :

F-D (sa riDoreEysoro

rocrpr.rM RyroM),

rotty BE' = AE . FD.

2AM:AK<AB+BK:AB+AC, 3Birc, BrnnrBac. '2 l-./rt.fi^o

;!:'iJt -..lit,

AoB)rrnIIa 6yAb-nnoi croposr.r rpsriyrHliKa Ee 6inbIIIa,

1. Bvav€Mo sKrrfi-He6yab rpn&yrlrlrR -4rB,Cr, noai6strn : 7O' , Bstr!u]x AaroMy sa ABoMa ltyrarr]d lAt : 60" , z4 AoBiil,Erfi BiApi3oI( AtB1. 2. Ey4y€vo 6ireRrpL{c} k}'ra a. Boua Hc aopiBHIo. naHi-i:i

Meaia\ta CM

Hiri

cyMa AoBlKrH ABox

C, - 1".

Go' Dllo ',o'

l!r: rEoMETPtt Eypaa M. t", TapaceHKoBa H. A. t:;litil:ii:iliifLi:::li:::*

cr,

l\:

Ea3rir,

2) fioain]rBlntr Binpi-

n-_r

6y-

ay€Mo MeAiany CM1. 3) Ha npoMeEi CM1 BiARraAaeMo rinpiaorc

CM = m,. 4) IpoBeAeMo

flpr

o4epxytor6 uykaHy OrrlTy. Haiqacrilne MeroA troAi6Eocri BnKoprcroBvor6 y 3ara.rax IIa no6yaoBy,

7O".

Box -4,8r

M€roA roAi6Eocri poBB'ssyBaHHi Ba,qatr sacrocoByrorB rremoo noAi'hoc i. IlpoBoAsqrr ana-riJ Janaqi. Binr.,rna@T6 oAFy J yMoB, qo xapal{repuo\c po3Mips Iny&ar{oi ibiryp{; 3'acoByrorr, cno.rarrcy Morr"'rfiBicrr, [o6yAoBrr Ee EyfiaHoi {biryplr, a noai6soi ao Hei, IloriM 6yayrorr, AonoMi}KHy Oirypy i rdAAarorb ii treperBopesFp [oAi6EocTi Tan, qo6 BnRoEy3anscb BiAKnHyra yMoBa. flpE qboMy

tcBAt :

m..

n06gAo6a. 1) Io6yAy€Mo M1-B1C aa aBoMa EyraMr ZA1 BssBrrn AoBinr,r]ti BiApi3olt.4rB,.

19. 4.48, o AACB 3a ABoMa xyraM'{: ,1A ZACB s ytroBojo. - crLnt ]Jun, IABD: 3 trori6Hocri rprRyrsHl(iB Bntr,IrrBa€ EponopqiiiHicrL BinnoBi4Hrx cT opiH: AB : CA = AD : AB, saiaKta AB2 =-CA AD,

736

il;ffi;;;;;;il"^'"i,irili-"'Ji" " -",

22. AnB. nnaH no6ynoBtr y N! 21. 23. ga.qaqa oropHa. /a'ro.' Ilo'yAasamu: LA.BC rat", t\o ZA - u, zB :

AC.

ro saAa'ra 3to-

II06yA06a.

goseae\H$,. A-B Il A,8,, 'ro[y zcAD : tcADl : 60", ICBA = CDE - I, 4 cM, tlo6y4oBaFxii rpxKyrE x Bi,qtroBirac B.iv ,Sanaqi 2) i 3) po3B'Eaylorr,cs aqanoriqHo.

noMBK. '

HepiBricrb rpurcyrunlta

3 ABoMa 3a{anuMn llyraMn noAi61{i, 3a aBoMa lr]4aMs i Ha_

cryrEoi no6yAoBr ioro 6iceKrp,rclr.

iil.-.'..1.11.:.1

rij+:.:.:.]:.:

rpr&yrE[na

6iceKrpnci 1". 3. Ha rpoMesi Cr, Bial{na,qa€Mo B,iApiso:{

18. BiAKnsAeMo sa npo,AoBJrreHIIi :lIeAi,a]JL, AM Binpbor. MK, pi!'ltlil AM. Toai ABrC napanenorpaM (ra o3EaKoro). SacrocttsaBtxn EFpiBHic rb rpul{yrHxl{a

OcRinbxn Bci rpl4lryrErrrfl.r

lr.rTr,cs.,qo no6y,qonx

^ABC

.rep* roqny

.44

npsMy

I ArBr.

yl(axrln.

EoeeAeHHe.

AB 11A,B,, rol{y ICAB : ZCAP' = ct, ICBA: ICBA. : b CM: m", CM - \'eai.a' Ira AABC, ocninBltn npl, rapanen6HoMy npoe$rl'BaHEi s6epiraerbcs EporopqiiHicrb BiApisr{iB rspa-tre)tbllrx npnrrltx. IIo6yAoBaHtii rplkyrsnl( BiAroBiaa€ BciM yMoBaM

:ailtlitlifiillii;:i::.:,:ti rEoMErPle Eypaa M. 1., rapaceHKoBa 24 vci r,qP,

u.. !.

ti:!i

737

Ocl{irbKr.r Bci rprnyrEtrrcn b sa,qanllM BiAnolneHHsM ABox cropiE i AaIrlrM xyroM Mix{ Hr.rMr I]oAi6Ei 3a II osEarcoro, ro 3aAa.ra 3BoAlrrbcs Ao no6y.qo3rr rymtyrlrrxa , ,BrC sa croposaur roB,IrnEolo ta i r.D i nyroM Y MirK ErMq (r > 0 nosinbH ii Koeibiqi€gr nporopqifisocri). IXyEaEr.rii rpuEyrnrrK roMoreDqHlrfi ro6yAoBaEoMy 3 qesrpoM roMorerii C ,qoBxrr-rHa

Meaiar

i p=!!,

seminl

BiAnoBiAHo 3aAasa

Ha npoMeni oB I opt.

a. flpoBeAeMo qepe3 ro'rRy B BirpiroK

OrplrMaeMo AAOB. IIpoAoB)riuMo ioro cropoHr O-4 i OB 3a ro.rRy O flocniAoBEo s'€AHaeMo 'ro.qxLt A, B, C I D.

ABCD

ro6yAoBaua

.4-81 BiannaaeMo Brnpi3oK ,4,8

siaKna,qeMo OC

iOD : OB.

Ety(^'lvnr napanenorpaM.

noqeaeHHe.

ABCD

trapanenorpaM, 60 iioro AiaroHani nepernEarorlct

ror{Rolo

Eeperrny Ainnr!cfl sasnijl. A.4BC, y nlroro AC : BC : m I n, ZC : \, Lleaiarla CM = m.. 1) ByayeMo rcyr C, lC : y. 2) Ha no,o "ropoHax Biax,rdaa.Mo BirpirKx

24. Hexan rpe6a ro6yAyBarr{

nr i CB = nx tx

O.RinlRu

napanenor pav AB( D BlnnoB Aa( Bciv

Meaiasa,

2) fl06)aoBa

I cnoci6-

yrKoroAc I B(

n:n.Ats

4,4-BC

CM:

m" 3a ro6y-

(lC:gO"'J,

27, Hexan

: nx

AoBinr,n

€Oiqieur rporopqifi Hocri). Bu rioEaeMo roMorerib 3 4enrpoM Ci Roeoiqi€s'o* e = 4oB'r !a -inorFHv3 AooorvirAHoro M B a.

cnoci6.

BiA cropiE (yra, € ioro 6icexrp[ca. Orxe, nyRaHa roqKa X roql{a neperrHy npflMoi a i 6ice(rprcl{ Kyra /;C.

rprkyrllun

AC,-tsj (ZC,

pa-renbHy B, C, Ao repertrEy yxaHr.rii. 4,4-BC

roni

AA .._r' BC

AC. B,C,

A,t .

prBHosiraa

M i K, a

Ta'{ v ,rxHoM, roqHa Y, p,sHoBirAdlcHa Bin r fopiH roql{a repeRyra i piBr{oBiaAaneHa Bia roqolc M i X

t?l

ra nollvAoBoro,

ra 3Bo/ 116.F ao no6) roB/ -pvltyrLlHd rd BinHoureHHaM pEo\ ;o o "ropiH i {} rov M'x{ H \aY.

26, 3ana

Hexafi norpi6Ho no6yAyBarn trapanenorpaM

cepeaEH

H[ii nepneH,Arfty' ,!sp, npoBereHni ao BiApis$a Mli.

rrHy 6iceHrprcr ny ra,43C i cepeArHEoro nepneHrlrl.ynflpa Ao BiApisxa -trM (rnu]o rana roql{a icEy€).

npoMeEeM/C, y roqqi C.

noseaeH+'!. C,B, ll cB, roMy &4c18, N &4c8,

fMT,

neHrx BiA roqo't

Ito

6icerirpxca rrEoro llyra.

90') sa aBoMa flareraMu: /.C, i B,c' = z. Ha flpoMerli,4B, 6y,qy€Mo ro.rFy B raft, qo AB : e. ltepes roqlly,4 trpotseaeMo np.sMy, ra-

ByAyeMo trpEMoftyrsufi

i npcuy a, sxa repernHa€ cropoEr (yra.

aaHo Kyr.4-BC

28. IMT, piBAoBiAAareExx BiA cropit{ I(yra, -

'ra BP : nt (r > 0

MoraM sana{i.

IMT, piBHoliaaa,leHrx

no6yiy.rao nptMHii xyr c. Tla ;,o'o rropoH.x Bir{iareMo BiApiBXr ArC

ZAOB (t,AB=a.

Hexan norpi6tso 3sanrr.I ro.rny X, rRa 3a,qoBorEH.se ABi yMoBr. lMT, rqo 3a,qoq€ Oirypa I,, a IMT, trIo 3a,qoBon6H.ae Apyry, BonbHs€ rep y yMoBy, - f'r' IlIyKaHa roqRa X e ro.rRolo nepernEy Oiryp FL i -E,.

Hexaii norpi6Ho no6yayBarn flpsMoftyr rn

m I n.

Ieotnenpu\Hurr. tticttan no,ton (IMT) EaslrBa€rbcs Oirypa, nKa c&rraAaer6cs r ycix ro'roK nnourkHlr. tKi Malorb neBHy B,13.rl'rBi.rb Vl eroA reoMerptrquxx vicub

AoBirbHe

3) IinrMo BlIp'JoK ,4,B, "cBnii (M,) i npo BoarMo Me,qiaEy cM1. 4) Ha rpoMeEi CMr BiA roql.r C BiARraAa€Mo BiApiroll CM: m". qepe3 roql'yM rDosoArMo AB A1Bt. LABC - tljyv.a:f,:,1,:i,. IIoaeAe H'Lv AABC ZC:\,AC I BC: nt n,CM

25-

l1 :.4( t BD mtn. roAC: BD= 22

29. SaAa.ra otropHa. IMT, srii 3EaxoAsrLcs

Ira BiacraEi z BiA npnMoi

cyKyrEicrL aBox npsMsx 01 i d" trapare'lt srx rpeMiii a i BiAAa-leHIrx DiA Eei Ea Bincrar! n. fMT, qorlraroat16.''Ha Bianlahim Bia rornx M, , Ro,ro r up rpov t Toqui M ipar')cov.

€

TaKtrM qrsoM, InyMHa roqrca qe rorrKa neperEEy Eora 3 np.aMnMr ar i .,,.

2) BjnlinaaaeMo Ea fioro cropoEax BiA Baplnlr]Ill BiApi3ltn O/: m cM i OP - n ci (n6o n\ nx, ne r AoBlnBEe AoAarEe qlrc,'lo). OrprMa€Mo

Taxux rovox uoxe 6yru: 1) oAHa (riono Aorr(a€rbcn Ao oaHiei 3 np.aMlrx); 2) ABi (xono reper{Ea€ oAliy 3 npnMrx); 3) rpr ((ono reper Ira€ oAlry trpsMy i aoDnaerLc.s Ao iHrroi)i 4) qorllpr (Rono treper saa o6tABi rpnMi ar i a,). cnirbHxx roqoF i3 xoaHoro 3 Ept Saaaqa tre Ma€ po3B'ssl{y, ntitqo

BiAHoneEH.s fio.o AiaroHaneii,4C : B, m : n, xvr Mi?I{ HlrMn cr, cropoEa,4-B: a. Io6yAy€Mo 4,40,-8,, cropoHr.r snoro el,quocsrr- D : n i yrBoprororb (yr rx: c.E src '1 nyr cr s BeprxrHoro O,; 1) 6y,qy€Mo

, -BCr.

LAOBt.

738

!:it: I-EOMETPIg 6ypaa M. 1., TapaceHKoBa H. A. ::::.:i1:i!:lili:'*illi;:;ii;;;

i:::*i;ii:lftil::ilili;!irt rEoMErPle 6ypaa M. 244

1., rapaceHKoBa H.

{l:i

739

Pa,qiyc l{ona, npoBeAeEril y roql{y AorLIRy, nepr€EAlTl{yJl.spHni Ao AorI'rqEoI. ToMy qEETP trIYHAEOTO IIOJI& JIETIIITE l{A IIEPIIEHAI'KY' nspi Ao EpsMoi a, npoBeAeEoMy q€pe3 ro.rKy B Oc&inEKn Rono npoxoAtrL qepes roqlln .4 i B, ro

30.

35. 1) P$MicrrMo rp[riyrHrrri /-BC B crrcreMi xoopAr.tHar rar{, qo6 fioro Mana rani &oopAnsar[: ,4(0; 0), B(12; 0), 41. cepear.rEa BC, SlraxoarMO rcoopArrHarlr rorrl{n -ll{ 3a rbopMy,'Iolo:

t-+-t^ 12+6 22

TaHnM .r}IsoM, qeErp O lllyl{aHoro Kona - ToqKa nepeTt{Ey fiepfiesaflItynspa, fipoBeaeHoro 3 rorrlirI

u, +

u= '22

: n.

3'€,qEerr.r BiAptur|aM'l roq.1'tt

- \f\ \t' ,y. =.rGt+n='6s t"*1.

3 Ro-

4+0 !t: ^ - =

A i B ra B i. C.

3 KonoM

MBC

Kono pa,qiyca fi ra xopAy Ac - d. Ilo6yAyeMo 'rep$ cepeaqEy , xopAr /C cepeAnEsEn trep' fienar.rftynsp. ToqKy B jioro neperrEy 3 llonoM 3'easaeMo 3 KiEqEMIr xopAr.

32. Io6yay€Mo

MBC

lrlyl(allri

B.D € MeAiaHolo) B oclroBoro paniyca -4.

A.Eartu. IlpllrlycrrrMo, qo rpn&yrtrnl. no6yaoEaHo. 3 ManmEKa B[trrro, rqo Br-rcora /, i cropoHa .r oaEosHaql{O BI'sBATIAIOfE rIPSMOIiYTHI,Ti TPII]TYfEIrII. BBiACIZ Br4EnnBac cnoci6 do6ynoBu. l. fio6yAyBarr opFvol(yrs fi rpuxyrRxn A-EA 3a rcareroM .4X : /, i ri[oretrysom ,4-B : a. Arra IIEoro 6yAy€Mo rrpsMnii lryr, rra oAEii 3 ioro c{opilr BirKnan€Mo Biapfuo& EA = /r. B rorrKt -4 paaiycoM a npoBoar-rMo al'ry ao rrepeT{I1y I ap}Tolo cropoHolo

33,

i!:

:ii ,

rptjftyrHrn (Brcora AC : 4, Bnscalll-rfi y Kono

piBHo6eapesnfi

i.!

"'r 9:r:.1.:.:{

ll:::!.i'-:rl ::,-,:i.:.ln

F!:i::;i!:

li:.i:.:.:.:

rpsMoro

1cyr.a B

roqqi B.

2. IlosHsqnMo ro.r(y, - cepeAaHy,4i 3. 3 ro.rKr, paniyco}r - rrpouoo"*o ay"y,qo o"- A perr.rsy c rpoMeEeM

A4Ja

AE : h -

llryHaHaii, 60

ro.rqi C.

AB a. AD n

- x,l,

+ (y"

- u,r,

AB=JA-4r" +(6+2f = .,F * d = .,tao * on = '4oo = ro; 2t AB=\F at'-tztzt =v[ 3f I '6*ro = Jze er u on = ,li' t tt "Es * r an = Jros r:.

34.

74O

i:i:::

BiAnosiAb:

+ a" =

f t6' ' 2" ryH(ry

1).

0+6 ^d: .lvjldl -._^ !tr; ^. --

3"tz kO.

l) '6B

3'E

cu; 2)

cu.

36. PosrdicrrMo orcreMy rcoopArrHar raKrrM rrrsoM, 11106 Beplnrlrll MBC (zC - 90') Manrt noopanllarri a(0; b), B(a; 0), C(0; 0). }lexail M(xi y) cepea{Ea ritroreny3lr.

a+O a 22-22

O+b

la b\ orxe. Ml-: \2 2l

SEai,qeMo BiAcrani BiA ro.rRl., M ao ro.ro& A, B i C aa &opMyroFo

.[,, 4'\ ts, \\"

^,=w-cq BM= CM= OM<e,

Ja"

J"" -

ffirt

AM: BM :

CM. CepeA[Ha riroreHF {

piBsoBiaaaretta Bia BeprnrrH rpnrcyr!{rrft a.

Aour*inny BiApi3Ha AB, ae A(x1: g''1, B(t:': a"J, o6qEcnloeMo 3a OopMvrolo AB = .l@,

veAiatsa. lpoEeaesa ao cropoHrr AB,

BLrcora, flpoBeAeHa .qo cropoElt BC.

2"2

y roqqi B. MaeMo

yriaEdi.

2) nosclle]llls aEanoriqEe ItoopAnEarv ro.rEn M:

3. 3Hafirr cepe,qtEy , BiAphRa.AC. 4. B ro.rKr D pa,qiycoM m rlpoBecr]' ayry ao nepernEy }tre(iary DB

v' = 94 = z, tttrg, zt.

Ar,t

31. finaH no6y,qo!!r. 1. Ilo6yAyBars &oro pa,qiyca R. Ilo3lra.*ir1I Ha IrEoMy roqlry -4. 2. flpoBecrli sa aonoMoron q,Ipllyns 3 roq&lr ,{ AyIy pa,qiyca b Ao rleperlrHv roM y rorrqi c. MaeMo cropoEy.4c

H(6; Ol, C(6i

,4-B xopaa qr,oro l{ona, i iioro lreHrp ,ex!rrr' Ha cepeArrHHoMy reptreEAlrKynnpi Ao xopAtr.4-8.

B Ao trpsMoi a, i cepeA{HEoro reptreEAtrKy,lapa xopnt AB.

Beprnssv

fEOMETPtg Eypaa M.

1.,

Tapacenxosa H. A. rt:j:li:iii;iii:*;i::i:i::i:i::

37. Po3Micrr.rMo AaHr.fli npsMoriyrrux ABC, B or.revi kooprflnar raxnM ,rxHoM. uro6 fioro BeplrrrEn Marr raRi xoopAznarr: -4( a; 0), B(-ai b\, C(at b), D(ai O\. Ilexait M(x; y) - AoBinbEa ro.rKa rnoqnHll. 'lo4i MA' + MC' : (t + a\' + y' + (t - a)' + + (y - br't MB'+ MD' (r + ar' + (a - b)' + + (': - a)'z + a'. MaeMo'. MA' + MC' : MB' + MD', rqo i rpe6a 6yno AoBecrr.r.

ilitl:itii:ift:::i::!:::i;: rEoMErPlt 6ypaa M. L , TapaceHKoBa

H. A.'i..1:) 741

yBeAeMo cvc'r'eMy KoopaEFar r KoopAr.rrrarr: ,4(0; 0), B(d; b\, C(a

38,

,(c;0).

AC,: (a + c

O),

+c2+b2.

BD,:

a), +

qo6 B€pmrrEI{ napanerolpaMa Manu

+ c:

+(b-O)z-a"+

br,

2o.c

nt =.n,1 \nn

b), : c, - zac + a, + b,. + 2ac + c' + b' + c' - 2ac +

cyMa KBarparis 4iaroHanFfi napane,lorpava nopiBHtoi cropir.

Bepnfllll rpatreqii

clvi l(BaAoalis iioro A.BCD (AD ll BC\ Mantl

Koopansarr: -4(0; 0), B(c; b), C(ai b\, D(d; 0\.

l:X

.ili1 li, :i;

.1,

I\S

160';

t:40".

z4z *

12:24(cMr.

1111.

1.,

r:3(,>0). BO:2 .3:6 do

-.[en"

(cM); OC

66:

6! :

42:

t:7.

(cM).

lO cM

iAC I7.v. A

BO'.

: 5 3:15(cM).

no" =.]to"

-t'=e

@*1.

i nt.

Po3B'rrieMo qe piBH.sEHs:

,,"= nxJn'-ss 2

25: nr. ft

\1100

mx +

poM6a o6'rlIcnlo€rEcF 3a

25:0; D:

8St

;

64 10 6

^2 , 2 a-8=10 8:2(cM)j n

-'^ 2:10-2-8(cM):

Biqnosi.Ab:2clIi8cM.

,i\mn . TapaceH(oBa H.

t cM i (rt x) cM flnolqa Ittrn-tt.

poM6a ro3Ea.rlrMo

l,/.d". s {hoDMvroro s 2'2

ftoeQiqi€Hr nporopqinsocri. ToAi cropoHl' npFMoKyrEdlia mJ.

fEoMETPtg Eyp43

: AO' .I BO'. AO' : AB' '

oa ro+o Il x,=ro+,4oo 2

7'14(cM'i

sfti x

: 5r.

45. AiaroEani

cll, 14 c\t.

nx nx mnx'i r'

24: 3:21

6x +

BiAnoqiAb: 1\ 6 cM, 15 cM; 2) 8 cM.

t, roai neplxa - 2t. IepsMerp rpIIl{vrHt' cropoEa rprltyrrrrlla r + 2r + a : 3t + a. P : 3x -+ a. 1) 35 : 3:r + 5;3r:30; r.:10;2. 10:20 (cM).

42. llexan x

g AAOC AC' = AO' + CO" AO' =AC' CO'. AB2_BO,_AC2 CO,; IO, (2r'),: 17,,(*cfi - 1OO - U.'z - 289 25/; 2.7x' - lagi t' :9;

BiAnoqiAb: 7

16)

(r+8)+r+(r+16)+3r-66; 7 + 8:15 (cM);7 +16:23

3 LAOB AC'

41. Haxaii Apyra

3)29:Ar+ 8; 3t:21; t:7;2

IIcropoEa-xcM III cropoEa - (x + 8) + 8 = (' + IV cropoEa 3t cM

Bi.tansi.l6: 40".60 , 80".

BbnBidb: lO c\r. 20 c!t. 2\ 43 - 3t + 7; 3t : 36], k:12:2 BidnBidb: 12 cl''. 21 clI.

43. I cropoHa -i (t + 8) cM -. -

npoBen.Mo ABi noxunr A-A IpoBeAe;o MO I a, roAi BO i OC Bj.qroBiAHo ' npoexqii roxsnrx .4,8 i -4C ua npauy a. Oc(i,lErcs 6irbEifi loxh'rin BiAroBiaae 6inLua npoel{qis, ro BO '. OC = 2 | 5t BO :2x,

CyMa rryriB

44, J ro{Kr A 40 npnMoi o

Or]I{e, cyMa KBaApariB AialoEaneii rparetrii aopiBsbe cyMi EBaapariB 6iqIrux croprF, AoaaFi; ao noaBo.Horo ao6!r*y ocuoB.

rprliyrFr$a 180'. r + 2t + a + 20": 180'; 4r + 20":180'; 4.r: 40. 2 - 80': 40'+ 20" : 60'.

P 2(m +

(cM)i 7 BiAnoqidb: 7 ci{, 15 cM, 23 cM, 21 cM.

AC'-a'+b!. BD' (c !t) b, c, - 2cd d' b . AC'+ BD'- a'+ 2b'+ c'+ d, 2cd. (l) AB':c'+b'. DC'= (a d\'+ b'z: a' 2ad + d' + b'. BC=G-cf =a c (a>c). AD' : r1"; AD : d.. AB, + DC, +2BC.AD: c'+ b'z+ a' 2ad + + d2 +b2 + 2(a c)d: c'z + 2b' + a' + + tl2 2dal + 2ad 2cd: a, + 2b, + c, + (2\ +.l'z 2cdBupasu (1) i (2) oaEa(oBi. 40.

\mn

.Ei. .F. ! n \l n 2) P : 2(nx + nr) - 2r(m + n); Pn Pn 2(n + n) 2(n+ nt -PmPn l3ulnoaldh: 2(m+ n') 2(m + n)

(b b)" = c". cD,:(a+ c c), +(b - o\, - a, + b,. AD' : C'. AB, + Bc, + CD' + AD' : a2 + b2 + c' + a2 + +br+c,:2(a,+b,+c,). TakrM .rnHoM, -4C' + BD' : AB' + BC' + CD' + AD'. rqo6

'{n

utanoaidh:

AB'z:d'z+b'z. BC': (a + c a), +

39. yBereMo crcreMy noopAlrlrar rax,

\mn

ls trj

: a2 +a,+b,:2(a'+bz+c,).

AC' + BD'

IF E; =-l-.E;

mt=m..1-=.1 \mn

i:ili:ii!i:iiii',:,::;;::i:,i::::i:

iil::::it::iii::it!iti:::,':ii rEoMETPlg sypaa M.

1., TapaceHKoBa H.

!li:

743

J6?6 576

26 +

2t x,

{ "/loo '

26-'[676 -b76 _26. t0= t6 r,'222 26 18:8 (cM);

26-8:18(cM). Bianosiab: 8 cM | 46.

TecroBi3aBAaHHc 1. t. 2, B. 3. E.

;_r8:

s. Ac = JAB' 1

MN = rAC

18 cM.

IllynaHa B:.rcora ropa. OcKinEKr 1AX, 'to LDBC N AABK. C-tr

- C, .BDBC socrl rprrxyrEnr{rB:

: BC 70.2 IJD = =-=cos30" J3 Bc

3 roai6-

ats= BK. 90' - 60' : 30".

B LBCD| ZCBD

30" = zo -33{M)'

140J3

!q - 7oJE '"

piBEo6eapeEnnr, AD

AB = AD

33-

210J3

rii Iti

Bidnosidb:33

iii

.4€ d,Be

cD--; su , tg0 49. teB ' = !q BM cD BM rsg, teo=2; CD:A.NI tea:(BM + l}rtg dt BM:CD "AM tsfl

Blllcory Brxn, BlAcralrb

r}=

6cM

ro.{fta, I1pnMa i IIno-

4Eatre)rcar{t, nrretltarlr

nexa16 y 4alrifi nnoElrni,

c[.

OcnoBHi

Oirypr: rorrKa, rpnMa,

rlnorql-Ilra.

.nexarr.{ vix{t. rEaxnaraEHqo BiaHoDJesIt'r: At ciorLa Bnxiane nonor{enEs, r$e nprriMa€rLcs 6es noriqEoro AoBeaeEHfi.

Teopenta (1) 10 (tg

d:1);

(2)

rBepAnieEEs, axe norpe6yeaoaeAenra.

52. 1, 4, 11. 53. 1,3,6. 54. Prc. 47 niapy.rsl,Iia: l\ A. a, B e o., De q

2) (ABD)i

2) (BCD\;

3\ BC, CD.

P]Ic. 48 riapyqsufta:

ro:

Be s.,Ce s,De d;

55. Prc. 49 niApyqH'lRa: 1) M, Nj Prc. 50 riApyqElrlla: 1\ P, Q;

BiAnosiAb: 53,6 \r.

l::i: rEdMErPre Eypaa M. r., rapacenKoBa H. A.

50. 51.

cD=-1 ,=,: , = 52,08 (M). tg 50" I 1,192 - 1 CM: CD + 1,5 - 52,08 + 1,5: 53,58 = 53,6 (M).

744

OcHoBHi

i (2) CDI

cD cDtgp -Io:cr{rcp-

t"*1.

rreperr.rHarorEctr tro trpsMifi, fiRa [poxoAl-rrL .r€pes

i.!?i:..r: faI{I{M.rnHoM, Iqoo t[Mrptrtr Bltcory AepeBe, norploHo aHarr[ ir.,i:.-t:: Br4 roqxu ftrocrepexeBst ao Brxlt ra Io aepeBa. tir-.!:il i:::#:* 48.,48 500: rg 9'= 500:0.1583 = 3158 ru. 3,2 rv.

tor

utIIlIi; fiI{qo.4. e c[iB€ q,ro,4l9ccr. ArccioMa 4 (rpo nep€rrn ABox nnoqrlr) 'fiK[ro aBj rl.nornl,rHn Marcrt cni,runy torxy. ro soun

':).:.-,:!1.!

!2=co

AricioMa 3. fixqo Ani rovrr EpnMoi nelxarb y nnourrhi. ro i Ico'r{Ea ro.rRa qi€i rp.{Moi neE{urr' y aaEifi rro-

IIopiBHneMo 3EsqesHs Q)

Ar.cioMa 2 (icEyBaEHs i eAltsocri rroulz sr) qepe3 6yAr,-.Ei{i Tp]I Torrran, 1qo tle rex{arE Ha oAHifi npsMin, Mo)l{Ha npoBecrr.r nnolqllHy. iao roro

,"'.

47. Atq L BC' AC L BC1,'rovry 4C1l AC. Toni MBC - AA,BC,.

:il

Js+16

rR cepelHr,rini' MCD.

POSAN 1. BCTYN AO CTEPEOMETPfi 1. OcHoBHi noHrrrc ra aKcioM]l crepeoMerp[-

IcHyror6 roqlrH.

= ZO,lg

3cM

i ro.rlc[, lIIo se ne]riarr, y Eiii,

BC ?oJ3 o,*.. sr =BDB lo 3 - ros r'r. = I4OJ3 cK = BK BC:105 - ?0:35 (M).

'i1

* te = s t"*t.

ArNcioMa 1 (Irane}I{Ilocri roqfttr trnoqnHi)

DC,

DB 70'6 , 140"6

2.5

=.,6'

Ar|cioMr crepeoM€rpii

DCA

AADC

+ BC"

OcnoBEi BiAHoDreEEs Mirrcr, aHarinaAaEHfi r.

Itt,

+ a'z =

OcEoBHi Oirwr-r B Dpocropi

= /CAX 30" ar( BEyrpiurEi pirEocropoEHi. IBAC : 1aO" - (ZDBC + ZACB) : 180" - (30" + 120') : 30'.

M(4 ol, Att[ = ,le+ \' BiAnoqiAb: B,

itittJtlliii:iii;iiii:ltii:

"4-B.

MN.

2) PQ.

:::t:l:;lltllilttii;:.::.ii:i::,::l rEoMErPle EypAa M. 1., rapaceHKoBa

H.a.

ll:i

zas

I 66. r{ep$ rptr aaBinbEi roql(r rpocropy

3aB}r{an Mo)rcHa rlpoBecrq nnoqnHv. roqlitr He nelnar6 rla oAHiIli rpsrvdn, ro 3s a{cioMom 2 ra(a rnorqrtra €ar a fit{qo ro'{Rr nerrarl' IIa oaEiii rpnMiii, ro raKrx nnorqlrll - 6esniq (a(cioMa 4) r{erBepra roqna ile BaBrrlat ,te)rlrrb 3 iE I{MI{ rp6oMa B oAlrii rrrolqxHi ToMv qepes qorrpl, rorrEn ruloqrEy MoxGa npoBecrrr roai, 1{o 'r BoHtt Harer{arb oaHj* nps qo6 qepes HItx Mo)nIIa npoBecrr'I ABi rpnMi' Miii a6o po3rarroBasi qo neper .ralorbc!.

56. ToqKa, rlp'lMa, rnorqtrEa. 57.

t,2,3,4,

gKrro

5, 6, 9, 10.

Prc. 52 niapyqErxa:

59, Prc. 51 dApyql{r.IKa: 1) Ae a, K E cr, M e

1)Aed.Kes,Nect,MecTi 2)Ae 9, M e pt 3)Bed,Qto.l 4)B€ B,r€ 0,N€ B,@e 9.

a.;

2\AeF,Kqp,Meg; 3\Bea,Nea,Qe&i 4)B€P,N€8,8€8.

67. Hexaii A. B i C - rpr roqHl'r nona, .tKi netriarr, v nnoqrEi a. ToAi xopAr AB, AC i BC ner{ar6 y tnonll'si s (all-

60. 2,4,5,7,9.

rpr.r

cioMa 3).

sKa treperrrra€ nRi-He6yab aBi 3 rpoBeaeHux xopA, Ha rpnKna{, -4J i AC B roqllax N i -ll4. OcllinrKu ABi ro.rliE M i N qi€i xopAr Ha-treJ{arb cl' ro

Bi3BMeMo AoeinBHy roqKy

i Bcs

BoHa, a

Ha Roni

npoBeAeMo xopAv'

3Ha-rnr!, iro'rEaX Harex{nrb

uolqlrsi

(:[

(aft-

cioMa 3).

68. TaI{, rernarB. npoBeAeMo.repe3 rp.sMi,4-B

61.

:ii

iil

Miclfir!

69, TaI!, re?I{arb. I{ot{Ha rapa BiApi3KiB, trlo ne perDEar-orbcs, Br3 aqa€ €arEy nnorqlrlrv .t (HacrrAoh 2). To'rK" A, B, a i D HalPxsrb lr'ii n,rour Hr. ToAi rJ 6k.io\4oro 3 s.i nptvr. uro

\AC.o.,ABe a,Bceo.

'i'

s-Io

Hexafi np.tMa (, reperl'IHa€ cropolrr rivra B roqr{ax M i N. Toqi npsNla d Mae 3 nnou{trIroIo c[ ABi crin6ri ro.rl!tr. 3a aKcioMoio 3 q.s npeua ,le)rcrrb y nnonlqHi cr.

llt

t:l )

i BC,

cropoE' rcyra,43C, rl,'lorqslry .r (Eacriaorc 2).

aHcioMolo Eaner{rHocri npnMoi trrorquEi (alcc g cr€peoMerpii)' slcqo np-EMoi naner{iar! nrloqrni, ro i Bcs npsMa Eanexrr6 Iliii rnoE{rEi. ro.rEtr aBi

62. Hi, 60 sa

'L i'.':.:-:.:

I{acniaKr 3 a$cioM ca€peoMerpii 1. qepes npnyy i ro,rl{y, r{o Ee n€r*{Irrb roro ,n rinbr.r oAHy. 2. tlepcr rB ,pr\4i. oro neoelxralo

1i;.!.1!-\':

,1i:.!:.i:.:

Hin, uoxua nporecrir noorq"rrv i,qo npoBF.rr nnoLLr") i

,o roro

3. qepe3 6y,qb-sny npsMy B Irpocropi Mor{rna rpoBecru 6e3nirr nnorrnr.

63. Br3Haqalorb, 60 3a l{acniAnaMlt 1 i 2 3 aHcioM crepeoMer pii qepe3 rp.sMy a i oaHy s ro.ro( C i B a6o '{epe3 npnMi '4-B i. AC M AB I BC, qo neperl{salorbcn, MoJt{da rlpoBecrlT €at' lrv rnoqrEy, BiaMiHHy Bia cx. 64-

IInoqIrH' CninbHi ro.rRa

Cnii!!ra

65.

nDrMa

rEoMETPrg Eypaa M.

i ro'r(v.A MoxHa

trpoBecrlr

ruoriltrEy, ro3Haq Mo ii s.

3a al{cioMolo 1 crep€oMerpii icEye roqKa B, rqo He nex rij y IlJlolrtgi (} npoBeae Mo qepes npsMy 4 i roqRy B nnonll{Hv ll. fi,'Iorqlllu {x i B pisHi, roMy rqo roqna B nrorq'{rr p He ner{rrr' v rnou]nri (1'

71. IInoqrIIr o i 0 nepertEarorEcs ro trpEMifi o. 6ecr. IIpsMi a ib reperlrEaorEct B roqqiB To6ro

73, 1)

ix cninLHa ro'rEa. Ocxirbnr npsMa

crinllra npnMa nrorqrH o i P, ro roqRa

l+(oaHoi;

2) .rorrpq, 60 icEy€ qorrp,I rpinrcll roqok (ABC\, (ABD)' (,4C'), (BC')' Ko)Ilra

2\BeP; 3)C€(1,C€P. iia::

3a sacniAlioM 1 3 aRcioM clepeoMerpii qepe3 rpFMv a

72. lldB. dn.ioMy I nraHiMerpi rHa"lF)np^'1' rn qoll i rpFMrx).

1) A€(;

246

Aasa nprMa. 3a axcioMoro 1 rraEiMerpii (satelcHocli ro'roE i npsMI'Ix) icHy, roqKa A. Lro Hc npi/rb Hs nptMi; {1

70. Hexan a

B Ta(on HareRurt o6oM nnorql{EaM.

(]i3 BiY Yi6 aill A\B Bic CrD KiB Mia AB

npoxoanr! qepes qi toqklr, B3.qri norapHo, ner(arb v nnoqllHi c

3 Jr(rrx 3a a$cioMoro 2 BII3Haqa€ ealll]y finoqr'rHy; 3) 6e3,'ri.r, 60 Kor<Ha napa roqon Blr3lraqa€ eAnHv npEMy r{epe3 sa HacniAl{oM 3 3 a}rcioM crepeoMerpii MonrHa npolecrn 6e3ni'r

1., TapaceHKoBa H.

A. l:.ilt::*{Jliii::::il;:i:!i:i'

:tiiflriliiliii:tiitliii:j rEoMErPle

sypaa M'

1.,

&ortny raftv nprMy

nnoljlrIr'

rapaceH(oEaH. A-

747

74. ,fiItqo nroqrElr {[ i

ro npsMiii PN, A'BpP\ - no npflIlriit MN, DDPP ro rpsMii P-K,.4.4y4r, ro rpsMin ML I ABCD- no npsMin K-L. y repepisi yrBopnBcs r's?sxyrHnft

no npaMii b, no DptMifi c, npxqoMy opflMi a i. trea n.lourrHx B i ] parlrnalorB.t B T oqqi A. 1o q'l roqfia Ha-rexHrb xo1+tHii B nepernHarorEc.s

MLKPN. 2) Ha Mai1, 77 ci.{Ea trnortl{Ha (MNK). BoEa neperrlla€ rpaHb.4,sB ro npsMifi Il.L, NM, rpal{b.4-BC no npsrpaEB BCS no rp.f,Mirii ML, rpaEb .4CS - ro rpnMiii Mifi NIl. y nepepiri yrBopr.rB.s qorIrprxyrExK.

is rpr,ox nrolqlrlr C[, P i Y. cri-,rr,Ha roqlra trrolqnll d i y 3a akcioMoro 4 HaneJflrrb niEii ix reperrdry: C e o.

83.

c, i F neperlrtlalorbcs no trpsMiii.. Ilnoqrsa y reperxEae nnoqlrHy (1 ro rpsMii o'

75. IlnoqliHa

trJ'lontrrEy

Heran trpsMi 4 i b nepernHamrl'c* B rorrqi A, roAi roqRa r{ Irane}Rlrrb KoniEin i3 rpbox nrorqlrE d, lliy. 3a ancioMoro 4, oc&inbl{r A € d i,4 € B, ro

Tax; 2) :dj,i B ocEoBi npaBnnbEoi [ipaMrAn

85. 1)

3Balrr{x qe

Mae

3) Iri. nen€Ttr trpa3rlnl,Etri Mllorollyrssl(, cepeA na

KBa,qpar.

86. 1) Hi;

Iri;

3)si;

tr{o6 dpaMiAa 6yna lpaBnnhEorc, norpi6Eo, B*Inblrr4fi MnorcriyrErrK i 6i'rHi pe6pa 6yrxr piBHrIMrI.

kd\

uricrb:

a) rax. qo6 y ii ocsoBi rexaB npa'

a7, y rpaBnnbl]in EipaMiAi ocsoBolo Brcorl e qeHrp Mlrorolcytllt lia ocsoBn (qeErp

rlocri rroqlllrn saBircAl nerlcarB Iiy ne 6yae xlrrarlrcn.

B oAHifr

arccioMolo

2 icsyBaHEs

nrroqlrHi. OrtRe' nlrarrB

€A'{y qboMv BirnaA-

i onlacaHoro ko,ra). y ryalrrbHift rprx{yrHiri dpaMiAi BDn.aHoro

rle rorrKa reperrHy MeAiaH (B*cor, 6icercrprc) roqKa rpnxyrnrxia ocsoBr. y rpaB:Inr,Ilii .ror{pl.rKyrsii rdpaNriAi I{elrrp oclroBri

repernEy AiaroEateii EBaApara ocrroBn.

Ancioma 3 Ha-re)+{Hocfl nptMoi onourrHi.

aa,

lIpnl(pitrnslorE Ao xiHqrB trporune)i{Htx Hixon flttqo Hnri'r repertHa' lorl'cs, ro 3a rlacniAKoM 2 3 aKcioM. crepeoMerpii Kisqi siniolr re}{larb B oAlrii rno-

?9.

A-BC.

nrs roro,

77, Kinqi Einio$ rrrarr'IBa qe rplt roq&1I' sKi 3a

78.

BBpp' AAp$' ABtCr

1) .4BS, CBS, CDS, ADS, ABC; 2\ ABS, CBS, CDS, ADS, ABCi 3) ,43S, CBS, CDS, ADS, ABC.

npoMeHiB BrsHarra€ rnoq rv. Sara"ra 3Boaxrl'c'l Ao triApaxysRy KinbKoc'i raxrx

^.,2

(Ap\C\ri

84.

76. Ico,rtna rapa

n(r, +

(.4-BC),

3\ A4C1C'

no trpnMii b.

rap. | ) {db), (o.), (bc) lp'{i 2) (abl, tac\. tadl, lbcl,lbdt.

2' A4C1C' BBpp' AAtB$, 4BtC1, ABC:

HITTKLI

urr4ni.

,'....... 5 2. npocriuli MHororpaHH]aKt4 Ta ii nepepi3M ;fi::i.ii eO. 1) flpfi3Ma a6o rapareienineA (puc ?3) ocHoB aBi,6i'rErx $auei B ocuoBi napa,eiorpaM a6o npsMonvrHlr(. Eiqui rpali - napare:rorpaMft ll:i.lii +..:.:.i:]t Mor{vrH[r(xr. 2r lllec rltyrsa njpa\dina rp[r' 741. ocHoBa l. 6icHx\ rpageii 6' 7$::ii: :i;ii.!ii:i octsona IIIecrI.rK)rHlrIr.EiqnrrpaHi rprxvrsxltr{ f?tiiiL, 3) rpxKyrsa nipaMjra lp c ?5r. ocHoB - 1.o;qH x rp€F"6 3 OrHoBa rptrHyrHxx. 6iqHi rpasi rpxKvIHhrtr. 81. Ao

Ma.r. 73:

2) ^rAA1,

AD, ABi i ABCD:

^)AAB|B Ao Mar. 7a: 1\ a)AB, AD, AFi 2) a)ABCMEF i ABD: ,qo

(nps-

TPI,II(YTET,IE

ffi

npsMorcyrHtK

i"...::.i.::#

B) CC1, CB, CD6) AB, BB' BC', 6\ ABCD i. DDPP: B) -

6\ BA. BD, BCI

BCD 1CDM.

B) CB, CD, cM. B\ ABD i BCD.

Mai. 75:

1\ a\AB, AC, ADi 2\ a.\ABc i ABD;

6) BA, BC. BD; 6\ ACD

BCDi

a) CA, CB, CDB\ ABD

I CBD.

Ha uaa. 76 uHol'orpaHHrl{ neperlrna€rbcs rnoflrullolo (,44Nr). li mnox uoxua ro3Haqlrrl' (PNM), (PI(I), (NI(L) rouro. Ci'rHa n"roursHa neperEna€ rpaHb,4LtBrB

82. 1)

748

TPITIiYTHI,IR

ij:;i rEoMETPlc sypaa M.

1., TapaceHKoBa H.

A. ::iii::::::i.:::i:i::i:iii::i::li:ii;j

rptt r(yrrrrrR

;i:::i;iii:i:t;:i.:iiii;li:!:i;:ii:: rEoMETPlc Eyp,4a M. I., TapaceLKoBa H. A.

llt

749

npsMor{yrEr.IR

npsMoliyrHr{I(

49. MlroroliyrElrll repepi3y roAi6sDii ocHoBi (3a B,'lacr Bicrb cepeaEEoi niHii)'

,^' A\\ 1 l\

/4,'

1A ( f-t?

vY)

xyrH'.rn

qoTnet4kyanttr

(//ft$\ 1) u_J/

1\)s) 1) Toqfi' M i N ciqEoi trjlorqrlrr re]{tarr y rpaHi,4-BS. ToMy Ei r1nolIlEstr neper'' llall)rbcs no npflMiii MN. MN Binptuo( neperr.rHy ciqHoi rnorqHn i rpaHi ABS.

ecrr(yTHIrIi

iii

AHa,roriqHo, ci.{Ha nnoqrHa repemEa€ rpaEi

90. 1) 5 rpaEefi, 6 BepulIll, I

qrcno Bep uH (B)' JIeoHapAoM EnnepoM 6yra BltBeaeqa rDopMvna' flKa 3B'n3v€ .padefi (f) i pe6ep (P) 6yab-s'.oro oflvnnoro MHoro.pass'(a npocrlrM ctrtBBla

tI :l

so.resuauB f

-!i::.!

:l . t :.-.:.1'

. 1) 2/1 (noaBo€Ea ftinbliicr! Bepln'rH ocHoB"); , h I (BFprL,,Hu o, Hoer repurs r nipaNal,ar).

92. 1) 3n (troAnoeHa ftin!fticrl' pe6ep 2) 2r (n pe6ep ocHoBr + ,'' 6i'rH'x).

ocHoBtr

+ raKa m HinbKicr! 6iql1rx);

95. Hi,

2) 8i

60 BpaxoByerbcs

qrx trnoqtrE. Ararori.{ro Pf ISz? DyRaErin nepepi3.

reperr.rriy HoBoro.

-i

BsraA$ax 2) Bep]nrllr{ C.

,riHin repert{Hy ciqFoi nnoqEE 3 oc'

3) 3aaaqa Ee Mae popB'.s3lty, nKnlo MeAiaHy rpaHi BCS npoeecrr

1O0. Ilo-nepllie, qe nroqrllr, sni Micr.srL rpaHi (y6a, no-Apyrc repepisr, qo npoxoAnrb qepe3 rportrne]{Ei pe6pa: AA.ClC, BB\D\D, AB{\D, A\DPB, ABC'Dr CDA,B,; no rpere, repepirtr, rqo npoxoarrb qepe3 r{irqi pe6ep, tftj snxoAnrr' r o,xHi€i BeprxrH : .4r,C, DA1B, Al3'C i a. A. 1O1" 11 rnoqtrE: MPS, MPT, MKS, MKT, NPS, NP?,

93. 1) n + 2 (n 6i.'Hux rpaHeti + 2 ocHoBD); 2) r + t (n 6iqlr],1x rpaHen I 1 ocHoBa); 94. 1) 8l

N,t i M-K

ryr{aHnfi nepepir. earHxii po3B'saoR. 3) MeaiaEa .pad SBC rpoxoArr! i{epe3 repruvEy S i cepeautsy p€6pa BC roqry P. To,qi SP ,riHi.a neperr.rEy ci.rEoi rrorql1Hr 3 rpaHHro ACS. ABi ro.rKrr S i ? cnir6gi roqnr ciqHoi nnonrnHlz i rpaHi.4-BS. ToMy S? "riE-i'

no BiApi3Kax

MNrr

Pe6eP;

2) 4 rpaHi, 4 BepIIlrHn, 6 Pe6eP

.:j :j

AS, i "1,8C,

Mrs,

NKf , MNST, MNPK, PKST. 3)

4)6

rirbrln liinBrdcrb

96. 1) BBICLCi ,rlCp; ABCD; A9ppl; 4 np$Mii 2) AAlB'Bi BBICP\ DD\CP, ABPpt 4 lip'rMi.

102. 33 nrolrlrEr.

,li ,ll

'li'lt

97. 1)

BCS; CrS; )4-BCr; 3 EPsMi; 2) ,4-8S; CrS; ,4rsj 3 rpsMi.

zso

r::..t

rEoMETpre 6ypAa M. t., rapaceHKoBa H. A.

liii;ii:tli:iil:liiiJiiiri:

:iajiiii:ij:;:.:.. i::tiliiii:;:, rEoMErPle Eypaa M. 1., rapaceHKoBa H. A.

iai;i

751

103. Po3B'ffasa 104.

riApt

PO3A|I 2. nAPAIEnbHtCTb npCMt4X I ntou{t4H y npOCTOpl

{Hr-rliy.

ABa Br.manftr.

3. B3a€MHe po3Miu4eHBr ABox npeMlrx y npocropi Po3MiqesEs ABox rpsMnx y rpocropi

a) grcrqo npsMi a i , y npocropi Marorb oAsy cniJl6Hy ro'rny, ro BoHu ncpcrrrHarorLcr B rri;

Kynon ni$ npt- urau Ha3 Barrbcs yrBopeshii

srrM! rocrplri Ryr (q). 6) IIpaMi, sna nepernEarorbcs niA rpsMnM r(y, roM, HasHBarorbcs repne aukutapt utttu: a Lb.

AO 6)

B),qBi oprvi y npocropi, qo ne}l{arb B oAlrifi

PoslnsseMo cxnanHiEr.ri BsnaAo& 6). Hexan Ea pe6pax rdpaMiA{ B3sro rprr roqnr M, N i P. Bi,qpisrcr .ll/N i NP - BiApiBxn nepepiry,60 qe cninbHi locKI,l ri{Hoi nnotqrHx j rpaseii nipaMi,4l4. SHafiAeMo riHiro E€p€Tr-rEy ciql{oi finoql,rEfi s flnoqrrEoro ocEoBlr. Ans qboro 3EafiAeMo roqRrr treperrrsy npsMr{x MN i -Ar, qo nerKarb y EnoIiIrrEi-4rS, i nprMrx NP i Cr 3 n,lourunn CDS. ruoqnHlr [poBeAeMo rpnMy qepe3 3EaiiAelri roqxll x i y - niEiro nepersEy ciqlloi B roqqi tr, a nroqlrlIorc ABC. BoHa rleperrllae pe6po -43 B ro.rqi ,1, pe6po BC 3'eaHaBur rocniaosBo roqlllr, orpsMy€Mo nepepis MNPft.

nepnerrAlrKynsp, trpoBeAeH{i 3 rotr&d

,4 ,qo rpnMoi o. O ocHoBa neprreHAnr(y,rrpa. AO BiAcraHb siA- ro.rKn 14 Ao trpsMoi c.

nnoqllHi

He rrepefnEaroTr,cs,

tuaparent@tuu: a I b. ABi trpsMi y rDocropi,

nili trroqlrFi,

a'b, b'c.

qo He neniarb B oAE&srBarorr,cs Nutwo6i.tt umu.

Bi1cma

b )tLbk napanenbHu u npsjrurLu EoBr{rrHa nepneEArrlynspa, rpoBeaeHoro 3- 6yar> sRoi roqr.lr o4Hicj nprMoi Ao Apyroi trpsMoi.

Ma,t. 88t AB x CD: B; AB x B& - B; AB x AAt: A; AB xAC = A, BC x AB : B; BC x BBt : Bt BC x AC : C; BC x Cq : C. AC xAB.= Ai AC x BC: C; AC xA-41: Aj AC x CC1: C. 2) Ao Man. 89t AB x CB : B: AB x AD : A; AB x AA; : Ai AB x B& - B, BC x AB : Bi BC x BB1 - Bi BC x Cq : C; BC x DC : C. AC x lt' - 4; 49:X 43 : A; AC x AD : A.

108. 1),4o

09. Ha AA1 L

BC,

)- AC,

AAt

Man. Aat AC

AB' AAt

I Bpi

BB1 1

10. Ha

111

B,C, roqo.

Man. 90: CM

. ArB- lli

112, Man. 88

I AB, KN I

BC. He Mar. 91t KP L CA, CB L AB.

1O9, 110,

,4C, Man.

89 AB,

Mar.

90 .4 ', Man.

.4-8.

113. Man. 88:,4.{, lBB,lcc,,A,B,) AB,Bpll BC,4q AC; CCj - B,A, CC, ' AB, CPt 'AA,i CB ' AA- B4 ' Ap' B4 - AC. Man. 89: -4-41 llBBj ll cc1 |DDI,A-BllA,B,ID,c,|Dc,ADIBc11Bg|ADr AAt - Dpb AA1 - Bp, AA\' DC, AAr - BC, BBt' 4Dp B& - Dg|, 84 - AD, B& - DC, Cq - ABb Cq ' A\Db CC\ ' AB, Cq'AD, DD1' 414, D4 ' B\Cr D4 ' AB, DD1' BC.

TecroEi3aBAaHHq 1. r.

2"8, 3. F. 4, A.

Man- 90. A-B - KC, KB - AC, AX Man. 91t AK ' CB, AC ' KB, CK

5. E.

752 ilt: rEoMETprq

BB\

Ba, cct Ac, acr alcr. ccr -LA,c,. Ha Matt. 89i AB ! AD, AB L BC, AD I DC, BC I DC, A,4 I BPt, BPt L DPb Dp1 J- 4D1' $Dt r 4Br AAl I A.B' AA1I4B1' AA1 IAD' AA\ r 4Dp BBI tAB' B&.L BC, 84 r 48'

cct.

6) HexaftM tAArAM: MAt=2 5. N € ,r,, DN : ND1 :St2,PeCCFCPtPq=215. Toqrir M i -M crdrldi roqKr ciqHoi rlnorql,'}Ilr i trJ1oqnII!L4-4,D1, roMy rp.sMa

rpaMa ix reperrrEy, a Bi,qpi3oK MN - cropoEa MHorolryrlrrRa nepeptuy. BiApisolt, no nKoMy ciqHa rnoqnEa repertrlrae rpanb ,rrC,C. Axarori.rEo NP IpsMi M-|r' i -d, nejriarb y .rno4r-rHi A4.1Dr, X - ro.rRa ix neperrHy; aEalloriqHo neperuny npsMrrx NP i rC, srii ne]tiarb y nnoqtrHi Dr1C1. Y - ro'r&a Toqni{ X i y ner.car6 y ciqtlii rt"'IoflluHi i B trnorqrEi -4-BC. Orr{e, qi rnos-{IrHll nepervrralorbc.s ro trpnMin Xy. IIE npsMa treperlrEae pe6pa-43 i BC Bi,qtroBiAdo B ro.:Rax -F i t. 3'eArIaBEn rocniAoBEo oAepncsEi roqlrr, orprMaeMo repepB MNPEF.

Bq I AB, BB1 L BC, BB\ L 48I r 4Bt, AAt L A$i

Eypaa M. t., TapaceHKoBa H. a. ill::lii:.1-iirit:i:li:::::i{:::n

BC, MC ' KN, 1\8, PK ! AB, PK

iitailt:;i:l::liiii:iliii::iiil rEoMErPle Eypaa M.

1.,

CB.

rapaceHKoaa H. a.

llt

753

120. 1) ,4'g - BC,

.114.

I) AB X AD, AB I BC, BC X CD, AD X DC; 2\ A.B, i B1C i Bp I i c \Db cpl i AlDt' A\\ i 4D \l 3) AA\ L Ap,, AP\ L 4Dt, AA1 L A\Br

- AB, SB - AC.

2) AS

BC, AS

CD, BS

CS'Ats, CS'AD.

- AD,

- AB. DS

CD,

BC.

BC L CD, BC I CCF CD L CCi 4\ CD j. BC, AD i BC, 4B\i BBi, Bp1j. BB,] A,B, i D,4, AAli DAI, AD J' DID, CD i DP'

I{}Tl{ B rpocropi fiyroM Mini npsMr{Mlr a i b BBax{a€rLc.s rocrprii Ilyr, sllqo rpsMi yrBopmlorr, ro

cAt)

crpi i ryni l{yrri.

Ityr Mixr riepreHllr&ynlrpHlrMlI rpnMnMr

t21. t) Hit

AopiBrroe 90".

Hyr

Mini flapanenBHrMl np.aMlIMIi aopru-

6 B oAEii nnorqnEi, roAi sa arccioMoro 3 rpsMi,4-B i C, urxHr. uro cynepeqHr6 Mrrvo6i}l{Hxx npflMxx.

ItyroM MirR MIrMo6b{tHIrMt npsMlrMr{ HaslrBaerbcs Kyr Mivi npsMuMn, qo neperlrHc_ 'orBcs,

ii;

4t 116.

122-

- 40) : 2 :

DiBHocropoHHiii: ocEoDi piBEo6eapeEoro rpsi(yrHlrtra);

70' (lrvTtr rpu

,-v/l

A,/t

diyxaHa sin.raH6.

3 .M a6o 4 .M a6o 5 cMr

117.

t-tl

cM a6o 2 cM; cM.

D /87 Kft{

ti| ti| ITITII

ii/t:'-:-.::.::,.:.

^lJ

C I

/ c/r--V !-/ ll ll

/ L-)1

/l K /pB

,l-.---.-l---.

119, 1) Mar. 88 AC

AlC b

- 84,

lt:::

Hi; Hi;

2) 2)

iri; Hi;

3) rax. 3) ran.

- Cpi

' Apt,

.rqE t AD'

.\D=\E +C DC,= ,tF + A

Ja'+ e"

BP \ - AA'; AC

rEoMErPte Eypaa M.

= ,18

ruixr

-4,8,

i cr. -B,C1.

Biacranb

"/io Jo' + s' = .fe6 + s1- =

Ja'+ o'

riacra*

Biacras; Mirc.4, i + ao =

* o-' Mi,rc

c. ToAi

BiacraEb

BBI

\6i = z,4s t".l;

"41?

ar =

s'41

(cM);

1c*y.

"4e "67 4 cM,6 cM, I cM,

z./ir c-, s'/is

3\ .15'*12' = J,l1144 = \46e = 13 (cM); = ,n.ttt - rz,E tcu).

'/r2";2"

a6o Mr'IMo6 r(Id

niapy'rEuF(a:

BC' B$1, BC' AA|

BD =

i DDr

zl G'**=s,D t".r. BiAnoeiAb: 5 cM i 5J2 cr/-.

' C$b

AB' '

CC,,

BidnoqiAb:5 cM, 12 cM, 13 cM, 12J2 cM.

AF''

CC, A'C1' BB,'

2) Mat. 89 ni,qpyqssl{a: ^81. B4' DC: AA1 - DC, AA\' BCt AAt ' Dpt, AA1 ' Bpr B4 - Dpt' B\'ArD" en, - ,to, cc, - A.D,, cc1 ' 44' c1l'AD' Cq - AB' DDl ' A'4' DDl ' B'Cr DDl ' AB, DD\. BC'

zs4

1) 1)

124. Io3raqrMo BrMipr rp.sMoRyrHoro napa,lenenineAa a, Milc pe6paM!,r.4,8 i -DC (,4,,Br i ,LCr), b BiacraHr, MIi& AD i BC (qDi BP), c aiscranr nixi A,D i AD (DC,i Dpl i r. a.t.

BiAnaBiAb:

118. v Bcix Brna,aftax neperl'rlrarcrr'cn

BC'

vaa. 95:

rer{ ne}I{airn 6 y qin trro

123. 1) ArBl i A\A, AD i DC, AB i BC, Dpl i Cp I a' a' 2) BPl i DDr DC I B1B, AAt i DP1, Cq i A-B i,t- a.

2o".

2) 5 3) 8

,qo Man. 96:

i $apa,renr'Ei AaErM Mt{Mo6ii€suM

115. l, 60". 60 LAXC 2) 60": 3) (180"

2) Hi.

1., TapaceHKoEa H.

A. tiil:lLiiti::'.:lii:ltiii:lir

125. Hexaii AA nepneHrr{ynrp. npoBeAeFrri i3 ro.nn B Ao npsMoi d, ,4 ocHoBa repneH' arr{yrnpa.

3a HacniA(oM 1 3 aRcioM crepeoMerpil roqHa B i np.nMa a oAHo3Ea.rHo Br3Eaqarorb Aesxy nno-

l::::tii{liiiiliiliiiii:;; rEoMErPle

Eypaa M.

1.,

rapaceHKoBa H. A.

::L:l 7s5

qifr nroqnHi' nBi ro.rBtr A i B rlpgMo1, qo Micrlrr' trepneHAl{I{vnsp '48, sane}$arL roAi sa a&cioMoro 3 EpsMs.4-8, a 3la'rxrt', i neprleE4uKvn{p ,rex(arE v llii nno_

qlrld.

126. He:{an.4 € d,Bea,Cea' IpoBeAeMo CD -1.4-B

rpsMoi.4'8.

BiAcraHb BiA

ro'r(tr

a noriM 3 iboovvnh S 2aAB AD =

:L.

sga]'ItF!tro

2) [poBeAeMo

s=.Et@L-tsx21-14x21 r:,-121 3.7.4

rEn 4

(cM,).

25 2 84 168 AB 13 13 21, = !a!l! 2' = 1e, s = fa(lo:b)oo rofi =6E rc*t. 7p 2!=2

'1''z'3

SHaiAeMo

127.

tt l6f "',

B'ma,qoK

Blrft,qoK i1

'2 - 6110 - e) = Jro- 5 4.

a 2: -4. e o l:

a'E

10!A

(cM').

BXrT

cltr

24 cM

8) =

Eca'lr'r: 1) Be3ri'r; l)

xoaHoi: 2) oAEvi 2J

3) Jl(oaHoi' 3) 6e3nic'

Ml'tMo6blcsi.

lpoBeaeMo,4rl ll BC! B rpaHi,4.4.1r,, ToAi -4r1 i AL, treperuEarorEcs B ro'Iqi O 90" (:(-yr

lr'.i,llc

AiaroEatnMl-r KBa'qpara)'

c, piBEocropoEEi*' 2) M,BC1 A1B : BC1 = -4rC1 sI( AiaroEani pieHsx tiBaapariB.

ZABC:60'. c D

top:i

CDAE

raparenorpaM.

8 cv,

rrorqy M-Bt sa ibopMynoo lepoEa:

C.EFB 21

A.,res

l-a-8.,4,F.

^^ 2 ^ 168

A],

= .,[16,7.

s = ga 1"*1.

84 -2:-u BE -2 13 -168,",,t3

ABi npsMi a i D IIe Marorb trapa"renLHrrMr, a6o MnMo6i$iE Mv.

2) 8 rap.

132. 1) npnMi r.4, i BCr

lCD,

134. Hexail

"".

2, 24 nep^.,4'rB. ].li]$ 113 120.

1) 12 rlap;

131. 1) 3 rapn;

npoBecrlr nrroqlrHy.

ZD9D :

s-," = J2(21-1sX21r4X21ls)

128. Ba ymoaoro npar'ra, Ee Mae cninBlllix ro'rori 3 rp€Molo d i Ee ne}IC,lrF' 3 EeIo B oa_ Eiii ruorqttHi. ToAi 3a o3Ea'renHnM trpsMi o i b MsMo6it{Hi i qepe3 Erx IIe MoxHa

130.

nepneEAr{Rynsp ao napa-

=8lcM)_

15+14+13

AB5

Bidnosidb:

-4-E

CD 15 cM, Cr Bt:21 -8:13(cM).

BiAnMiAh: 15 cM.

13+14+15 \t p=-=zri

BC, A] I BC cnirLr renr,H]rr. npsr{nx, r{o Micrnrb ocEoBn rpaneqii, BiAcraEr, Mini HrMu. OcftirElc'I Ba yMoBoro rpaneqis piBHo6itrHa, ro

-- BC-AD = {8+161 IJt= 22 3 LA-BI': Ar = .tEE - BF" = {! = .,1s.25 = ,E% = rs ("1a1.

C Ao

SEaiAeMo rnorqy 4.4'8C 3a ibopMvnolo fepoEa' 1

133. 1) y rpareqii,A-BCD (AD ll

3) ICyr Mi}'i rlpsMuMg ,4, i CC1 AopiBEIoe Kl-rY Midi rp.trM'rMs .4, i Dr,: 90",

crirEllrx

V neprro y BrnaIliy rpsMi a i b neniarb

ro.roK, roAi BoHrr Mol$yrl, 6yrlz a6o

oAFii rnorqgsi, y ApyroMy si

(3a

135, Hexan npsMi

a i D nepernHarorbcs B ro'{qi -4. ToAi 3a EacniAKoM 2 s aiicioM crepeoMerpii EoHI, Bn3rra.{arorb Aes]{y €AnHy x'Iorql{sy CI. }Co)riEa iElna np.rMa 3a yMoBoIo trepernsa€ RotrHy 3 rrpsMrrx d i b i IIe npoxoAnrr, qepe3 ro.r(y ,4, To6To Mae s n,ror4uxop o gai cninbHi ro-rKr. ToAi sa akcioMoro 3 BoHa HareBrrb r1norqrBi c[. TaKqM quEoM, yci AaHi

136.

rpsMi naiexarB oAIIii Enorq I:i.

H€xan Bepmmfl-r .9ortrpttl/-yr.dv1""a

ABCD I]e re}lra?r, B oAHiri rrorqrrEi. IIpoB€Ae-

Mo iioro AiaroEanr, AC.

Ilo3EaqrrMo ro.rKs Ar, .B,, C, i rr cepearma BiAnoBiAno cropiH AB, BC, CD i AD. cepeAEs niEin MBC, AP1 | AC, 'to(i, AlBt

A-8. =

L Ac. 2

,,Cr

- cepeAsr riEin D'C lACi D.C =!a1. " 2

AHanori.rHo

AACD, 4

.rorrrptlKyr'lvlta AlBg pt 48\ : : rrc,. Asarori.rEo, po3.nsHyBE'r rprrEyrrrrErr ABD i CBD, Moxrra Aosecrr.r, qo 44: B\C, AtB\Cp1 rapanenorpaMr ocKinbnll iioro trpornrerini croporn ronapso pissi. A qe osHaqae, rqo iioro ,qiaroEani - BiApisr{v Ap1 i Bpt - repernEarorr,cF i roqkolo neperrHy HaBdn. TaKlrM qnHoM, y

Ainnrbcn

,:iti:{i:ilil-:itiil:t',:lt rEoMErPle Eypaa M. 1., rapaceHxoEa

H. A.

i:!i

zsz

137.

PoBrnEIIeMo ABa Blrna-qEr.

y tr€proMy Brna{Iiy

qorrpl,Kvrns

aiaroEani

-48C, repcrrHaror6cs

toqqi O' roMv

141. Ilorpi6Ho npq&pinvrr ABi Hr-rrx]{ Ao riiEqiB nporr.rre)riHrx ni}Itox cro,ra. g&Ilro Hr,rrKr, fieperHyrr,cs, ro 3a rIacj A&oM 2 3 aIcioM crepeoMerpii xirlrti rliJrlorc reJ{arL B oAnii:i rnoqnEi.

sac,liAxoM 2 3 axcioM crepeoMerpi-i rpsMi B, i ,4C rexiarB B oAEiii nrorqtHi, i roqlcr.r -4, B, C i , ner{arE B Hiii. y ApyroMy BlrnaAfty rpoAo tcerrEn cropiH.4-B i cD DepervHarc 6ct B rouqi O. roai qFpe3

142- 1)

qi ro.rKr MorIlHa rpoBecr! €Ar-rlrv trnoqrsv. Toqr{r A, B, C i , rer{arb Ea qux rDsMr'Ix' a 3Hatrrrr"

nnoqnHi.

cnoco6aMtr, Apvrv (n - r) cnoco6oM' Kinb1j n(n "'; ocHinb#Iepe3 lioJrcrv rapv roqoK MoxHa rpoaopiBHto€

138. flep y roqliy Moxlra Bribparlt n Kicr6 npsMtrx Becrr ,'Isme oally trpsMy. Tperro roqy Mo,*sa o6patr (n

KrcrB

(n 2)(n - 3) . IrpsMlrx 2

3a.a-r6Ha

qerBeprv

2) cnoco6aMq,

n(n

xin6Kicr! nap rpnMnx

1)(n

-2\(n I

3) ctroco6axrr'

lrttME Aopit'-

prBHi ope-

MokyrHnrlr. Hexaii pe6po ocHoBIr AopiBErce a, roAi 6i'IHe 3 ABa

.: B. IEB B- . ,liz^' ' "

:ao = co o9.

"'ts.

^ 5a2+-5a: z- oJi '"li 4422 -.

't..-.-...,.

.o., . -2

148.

0.6i ,p oi".co" 0,6 53' rpE3Mi llrvxaHi

BiAcraHi

qe pe6po ocnoBu lBin-

craHr, Mir* flapanen6snMx 6iqH Mr pe6paMt)' Biapi pe6paMn o,qHi.r

ta tBiAclaxh Mia nporxnell{\t{Mx i EC, (BincraBb Mirr nporx,lP){Hxvu De6pn Mr pi3rrx ocHoB). 2CD DE cos 120'(3 ACEr)i CE'-CD'+DE' roK

2) oaHy.

147" Ha Man. 106i

2')

cosq'

v npaui,{hEiii n€crIrr{yrFin

145. 1) OaHyi I

B4 | cc,, A-B ll A,8,, BC

Apt

cos 'a,

'140.

o3HaKa napanenbHrlx npgMr4x y npocropi

Bp1' AC |

2) A4B\B; BBPTC; A,A\CP. Ha Ma,!. 107: 1\ AB ICD' AD BC; KN AC,LM 2\ ABC. Ha Man. 108: BplllBC AD; AB )A,8,) 1)

3 AEOa 3a rcopevorc tsocrHY.iB:

BC'= BO' 't CO' 2BO CO

TeopeMa (oclloBlia B,racruBicr!). qepe3 roqKy, sFia ne rexsrrb Ha Aarifi rpsMiii, y npoclopi Mo1llHa npoBFcrrr EprMy. uapa,rc,r6Hy aaHiii. i rinhHx oaHy. Ba?lt,rxBo! r{eper ,qBi napare.rLHi npr\ai Mo}llHa npoBec,n tr,roulfiHy. i .ao roro

1\ AA,

pe6po AopiBHroe 2d. ,11

4. Bnacrr4Bocri

OJEa{a napa"len6Hocr i nprvxx. ABi rpsMi, napanen6Ei rperin npsMiii, rapan€,'r,!i Mtu{ co6olo.

139. 1) PosrnsseMo M[Mo6ir{rii pe6pa, Iianpl'IKnaa, .4,4, i BC Itvr Mir{ liroe riyry B,BC, ocrcir]"tu BBtl AA,. ToEi ZBPC = 90". 2.) OcKinbtsn npv3Ma qp3BnnbFd. u 6iqnr rpaHi

Itirl'

4q.

IAC,KN ILM.

AAIBPi BBrC$t DDpPi AAtDp;

D,c, )DC:AA,11BB,l ABCDT

A,Blcp\.

cc;l

DD,i

OAHy.

ccr; l) OAse AD;

149. 1) ,4Ar I

2) BP]l DD..

151.

2) oAHe DDi

DPi 3) oaHe CC,. 3) Ats |

A1D..

Ba ocHoBHoro BnacrnBicrro napa-,rer6strx trpsMrx qepes aaHy rorrky npoxoaqrB Ine otlra fipsMa, napa-nen6Ea aasiri.

"rn

ocHoBx,

cE = ./E*tl

fzr

' zs - so

ACCI-0:

EC, =

$c3

BiAno6iA6:

7s8

2;.

"o"

60' =

sJa t"'

cz"

152"

A\-l \L=j

'tE

ro '4oo =

L E

t"*l

5 ctt, 5J3 cu, 10 cu.

il::: rEoMErPre 6ypAa M. 1., rapaceHKoBa H- A. ii:riiiliiia.l:::ti::t:::i:i:

:::!i::Jii:tiJ;tl::ill::ajt:i rEoMErPle sypiqa M. 1., rapaceHKoBa H. a.

tiir

759

ro Bonn nerRar6 B oArrii ruoquHi. Biapi3oR '48 ABi cnirEHi ro'r&1-r C i B, roMy re}ti netrctrtb v llii trnoqnHi' A.4BB, aa reopeMorc <Fa.reca C, - cepeA!'IEa BiApi3IG -4Jr. ToAi CC1 cepeAEt

153. oclcirbKv BBr l] ccr Mae s qi€Io rroqlrnolo

y ririn

(cM\;

q cc,=+=rc

@M\.

3) MNBB1

oAEo3lraqEo Bl{slraqalorr' nnorqrlsv Iltotr{riEa'4A,8 treperrHae snoqssy o no rlp.sMiii AlBr (aricioMa 4). TocKtl,4 i B raAr i B, ne'(arB

154. fiapa-'renl,Ili rpsMi.A.{1i BB,

y qifi nnoqrEi ToAi sa alrcioMoro 3 rpnMi.4-B iArBr, a sHaqrrb, i roql{n C i Cr neE arl y rno' l,lj:d|ji AAIB3a yMoBoro C - repeAnHa A-8, roAi C, - cepeAr.rqa A1B' 3a reopeMolo @aneca, B cepeAEs nillis rpaneqil .4,4.1-8,8. CCr

-^ ,2 A4+

:1,

cq=19Jl1?=li

cc,

=&i3?

2) AHa"lori.{Ho 1) trepepig

(cM);

(cMr:

= 2E (cM,.

ne'ItrrE Ea aanifi trpsMii, Mo}IlEa rlpoBecr,r oany i

Dprrvy. napajre,rbsy aaHifi

rinbKs oaHv

gRqo ABi rapanerbEi rpsMi trepersyrtr rperr'olo trpsMoro' ro BEvrprlrsr pr3Hocro poEHi

(yrr

piBEi (BiAroBiAsi

Ryrr piBEi, c]'Ma BlllrpiuEix oAnocropoHEix lrvri!

180).

.Er qo npsMa leper{na€ oAHy 3 ABox fiapanenbEl-rx rlp.sM[x' ro Bolra flepertEae i ,cp)'"i. flErqo rlpsMa nepfieEAunynfiplla oAniii 3,qBox napaneJllEnx fipaMlrx' To Bolra rlepneH,[l.IKvntpEa

i trpyri;.

r56. rax. Fkrrone*xlLsH'iM,asolHinnno

[-[--el

Maru l-'-7 l-j/----l "^p,*,* roclrv l - / cninb,rv

rrr.rHi. B iHnJoMy Bunanl{y npnMa vo)l(e

,exar6

3 nnoqxuoro. B ',(irloalry ,ri trnoqn'tr, rinr,&n

760

159. 1) CropoEi

-419 sft cepeAHn ,risifl 2) Ai€roEaii,4C sI{ cepeaEs niEi.g A.^ABS. CS. 3) AiaroHari,4, sr. cepeAHs niiris MrS.

160. yci trpsMi rorlaplro trapaienr,si. D oAlloasaqHo BE-

ocnoBsoro BracrfiBicrrc Ilepanenl,Hr,rx qpsMr{x y npo, eropi qepe3 toq&y C MoxrIIa trpoBecrfi TinLKI, oAEy

rperiii, napanenbld.

trapanen6Hi

rlo

15a. 1, Ats ll Dp1, AD,ll Bc,t 2t B,c,llAD, c,D ) BAI 3, BD I 4D,, BB,I DD,.

162. Hexaft'c - AoBi"'rbHa npsMa, naparenr,Ha rpsMin a, sria reperIrEa€ npnMy 6. npsMi a i , BrnEa.rarorL ItroIIInEy cr. [poBeAeMo qepe3 roqny C reperrEy trp.sM x , i d B nnoqrlri o rpsMy c1, rapanenbry a. 3a

roByrorE trapanenEEicr!' cropiE trapanerorpalva, ocHoB Tpaueqlr' cepenEBor nrHrl rpnRy?Er.rria ra rpareqii roElo.

qepe3 rocRy,

npsMol{yr1{rl&.

3Eaqeror]' AesKy nnoquay d. flp.rMa c nepersEa€ rrpsMy a B roqai .4, trpsMy b B ro'rqi B. ToAi IrpsanoqlrHolo c! ABi cninbEi To,rRI,' i 3a aEcioMoro 3 crepeoMerpii nexr,rr6 y trroElr-rEi d.

Anfi BcrasoBnesfis lapatenBEocri aBox rlpsMar( Tpe6a 3saiirfi_Tperro trpsMy' nrdfi napatenr,sa lco]{Ila i3 Aaxrd npsMr'Ix. flptr qLoMv uaii'racriEe Br'IRopxc-

155. ABi rpsMi,

161. Assi fiaparenbEi npsui o i

BBI

2r...=lqj9=? 2 B')

rpsMoxyrgri& (nporrnexc- piBli! i rapare"rrui, NM ,L B,C).

cropoHr-r

@Mr;

cc, =Z= 4,5

1, ABMN

dA-BBr.

D cc,=+=6

ri:

157'

=:BB,

cc,

3a yMoBoro,

tj::: rEoMETPlg 6ypAa M. 1., TapaceHKoBa H.

l-- ljtj

blll--=-l "t la ,: a.

sl I

i{ltli:;:ittilJl::: :i;ii

tpsMy, trapanenr,Ey o, A siaqsrr, trpsMa d B6i, ra€Tbct 3 llptMoro cr. To6To Ha"re}rrurb tr oqfisi cr. Otxe, 6yAr-axa rpcva c, rraparenLua a, rqo rrepernlle€ npsMy ,, ner{r-rrr, y trnoqrIli s.

163. 1) Hi, 60 s&qo c I a i c l) A, ro a l], (sa oslraRoro rapanenbrrocri npsMnx). Toni oprvi o i b nexarb B oIHifi rTnorqrHi, qo cynepeqsrb yMoBi. 2) He 3aBt&An. IIe IIeMo}I{nrBo 3po6nr[, EatrpnRnaA, nriqo oAEa s trpsMnx !aparenbHa nnour.rHi, B rxifi,rcxxrE npyra nprMa i roqHa. 164. Hi. B sa,4aci 161 AoBeAeEo, rlo Bci trpnMi, sl(i neperrrHarorb AaEi trapa,lenElri rpsMi, re*car6 B o4Eii nro!.IraHi. Ane qe EeMoxmlBo, 60 Ba yMoBoro AaEi trpsMi - MnMo6j)I{Ei i He nexarb B oAsit nroqnHi.

165. Ijexait A,B,C,,. Aanni nepepb pr"slItr.'fo!'L AAP,B, BB,C,C, ... I..apa,n€norpaMr{. Orrxe, A-B - 4Br, BC : 8,C,, ..., roAi MEororcyrHnK ,48C... -(ocEoBa) Aop\B'lvle A282C2... (trepepi3). lqo n rpe6a 6yro AoBecr . '166. OcninErcn ciq'ra nnoElnHa rpoxoAnrr, qepes cepeAirHn 6i.rHrrx pe6ep DipaMiAr.r, ro Bi,qpi3rcr, qo e croposarrr repepfuy, cepeAHi riHii 6iqEnx rpaHefi dpaMiAa

i nopiBHrororL oonoBxHi pe6pa

ocHo8rr.

:iuii:.:iit:jiilt:ii{::i:t rEoMErPle Eypaa M.

1.,

rapaceH(oBa H. A.

;i;t

761

MicrreM cepeArlE BiApisxiB 3 IliHrrsMt{ na ABox MrMo6i}Rrxx rp' MDx e EnoqrEa, naparensHa r{r.rM rp.flMrrM, rlta trpoxoaurr, qepe3 cepearrEy oatroro 3 rallnx BiapiaKiB.

171. IeoMerprrqErM

p=3.9=3 4=e r"'r, 22

2\'2P=4 !=2a=2.6=12

"=(;)r*=na=ru,"-r. (cM),

s=l4l'=e'=g \ 2l

Hexaii roqnr M i N Ha,lexarL MlrMo6in{I{rM nprMxM a

r"*'r.

I{a

AoBin6ny tr-KvrEv dpaMiav 3 BepuuHolo S ra .fiKa npoxoanrE qepe3 cepe.qlrEr 6i'IErx pe6ep.

167. Po3usHeMo

AS, B, - cepeAlrsa - cepeArna cepeAllEa ,S i r. A. cepqquHa CS, D'

IIanpsEnaA,,4r C,

BS,

niHii rprKvE]rrciB ASB, B 1

B.C.

- -BC. C,D,- cD Lr-a

q4 uqu o"ou"u", rqo MEoro*vr'rft r.6'" A'4 = B"c' = cD=..." = ],2'--' Er.rii .4o MHolo&yrnlrxa ocl{oBr 3 (oeibiqi€EroM

168. 1) v d,4ff8 rP

cepeaHs .'fni.E'

l:;

trepeptuv roai6-

rP MB. Ll

:.!jii!:.:t.

Aado Dapa eneninea

ABCD\BPpT

BC,.

Aesnri.rrapa.nenorpam.

TOqOIt 3 nJror![]roro c[.

roql{r.4, B, C i roqftax,4r,.B,, C, i rj.

IlpoBeaeMo s ro.mlr S rpoMeEi.repe3

Eni repernyrB rnorqnEy To0i SA

:pavra:r. B o.HoBi qtsol rpAr1" tro a napaierorpaM ,4,8C,

pepi3 qiei ripaMiAn.

d i D y ltoro cepearsi Q (3a reopeMoro oa-reca). TaxxM qxHov, ccpcAr,{r.r Bcix BLApi3KiB r KiHqeMu H6 npsMnx , i b nc)r{arl' Ha orni; opflMit 3a sacnia&oM 3 3 aKcioM crep€oMerpii qepe3 IIIo npgMy npoxo,qs$ 6egniq nnoqtli Mr.rx

i:!:; fEoMETPlg sypaa M- 1., TapaceHKoBa H.

8,4,,

rrprxyrErx ArBjCrr|

aoBoata Mo,

17O, Hexan AaHo ABi napanenblri rpsMi o i b, M e a' N e b, P cepeA'na BiApi3ka MN. [poBeaeMo qepe3 roql(v P npsMv c' raparenbHv npflMn}r a i b qs trpsMa neperlle AoBinblrtt BiApisori xY 3 KiEqsMr'I Ha np.s

762

172. Hexan

BirbMpMo B npocropi noBin6Hy.ocKy S i aepH\ nroJlu. Hy o rax. uro S s AJc i ndpancnorpaM He Ma, , rj" 6HHx

r{o,1,r1 | B'C, ' 01xe, qorrpxryru,{K A,a,r-,D .re1l{ rb B oaHifi nnourni i iioro trporz ner{cHi cropolln rapanenL_ si. 3Haqarb, BiH napanenorpaM. AHaioli.{Eo

ro.xrr M i Ir nerriarb y qift rnoqrEi), 6 sEa.{urE i trpnMa NX. Hexaii rpsMi ar i NX neperrHarorbcn B ro.rqi P. To,qi P cepeArtsa BiApi3na NX. fl&rqo Z roqira nepe' . rrEy BiApisKa XY 3 rnorqr.rHoro cr, ro rrnoqr{Ea rpnKyrHr.llia NxY, sRa Epoxoanrr, qepe3 rpsMy b, rapar€nr,Hy nnorqrni Cr, neperrrHae qlo nnosln:ry ro r-ptr[iii PZ b. ql{lroM, cepe' cepeAaHa BiApisria )rN, ro Z Oc&i,'ls(n P - cepeArEa Xy. TaKnM ar{rra Ko!(Horo BiApi3tra -try B nilrq-flMlr Ha flp.sMrx il i b rexc[rb y finoqlr]ii d.

173. Ile\ai, ABCD

,riEif rpElcyrlrr.Ilia.43C, rapaterbEa cropoEi,4C' C,r, cepeAEs ni{is rpnliyrl{rrlla ,4rC, reni

trapanenl'aa cropoHi -4C. 3a o3Ea(olo rapa'renb_ socri np.sM'x y rpocropi rpsMi -41r, I C1D1 napane",rbsi, a ol'l{p. nexarE B oAHiii flrouxHi.

HexanXiv

'foli ADt

169. Hexan ro.r|t',4.. B, C i , IIe nerItar]' B oalliii .cpearsv n,roulhHi. a A,, 8,, C, L Dt 'rop'H .rorrpt(yrErKa.4,BCr' Toni,4rBr cepeaEt ,,;.:r!:.1':.:.i!:.

d i b. qepeg

npsMi 1r, i b,, qo reperr.rHarorlcn, npoBeAeMo

'psMonyrHr.rnr, D,C, Da. Toai 3a orHaxo$ napanenbHocrj nprarrx y npocropi,4-B I DPr'Iaj,1'o:I.1- AB : D1c1. OcrdrbKr.r nporrner*iHi cropoEr.rorrpnKyrllnr'a ADQ 18 prBr I rapajre,rLHr, ro BrH e rraparenorpaMoM.

, l:

.epeA/Ha Bi4pir'

3 kilrrtiB pe6pa,4-B npoBeAeMo AiaroEani.4r, i BC, npoTrnerrcEEx rpasefi. I pa"i npqvoklrioro napa,re,'Ieoincr" Oc Kin "K rc AB I DC, AB : DC, I D,C, ll DC,

Y LMBC EF cepe,qEs niEis, E-F J MB ToAi 3a osEaKolo napaner6Hr'rx npsMlrx v rpo' cropi KP I EF. 2) AEarori.rHo, r-E - cepe/:4 t rrrF'itr LAMC, PF cepeAH.s ,lillis A.43C, ror.ry KE ll AC t PF I AC' a ,Ha,r'l16. KE PF.

:i1

npoBeaeMo rpEMi aj i rL,

B oAHi; niourxs'. Y qifi )sa nnoqxHj ,lelKvrb nprva MV (ockii"a/ aBi li

BSC, CSD, ... 3a BnacrrBicrrc cepeAnr'oi niHii

AB. 'AB.

AnoBiAHo.

aoBinbEiroqrirnpnMnxd ibBi,qnoBirHo. OcK'r6I{fl trpe\,Ii did flapa,rerbHi.

cepeaEi

BiAnoBiAEo napanenbsi rpflMr.rM Il€pepi3 nnoqtrsoro'

- a -q a.s cs D.s roAi;=;;=d.= os.-= =t 4Br Bpt, CjD,, ... -

MN. qepe3 ro.{Ey tr

OcxinbKn ci.rEa trno IrHa ,qi,!r-rrB r.o}IlIIe 6iqHe pe6po nipaMiAr y BiAIIoIneEHi 2 : I ro Jd roopevoo <Dajp.a Bi4pirEn. no srflx ciqHa nnoqxra npperrHa€ 6r,rHi rpasi qipaviau. napde" 6Hi po6pav ocHosr{ i Binruuarcrb Ha rpaHrx 1px

llyrEnllr, noAi6Ei rparisM. 3Ba)r{anq

vsoroxyrunr.

pp3}r 6rar ra,aaqi l67.6aqflMo, ulo no4i6HHi{ ocHoB:

B uboMy BHnarKy

r KoFQiqicHroM h=.:.

2+l

neoepir - uc

'. 3

3 rcypcy n,'raHiMerpii BiAoMo, rqo BiAHoureHHs nepnMerpjB roai6qrx Qiryp k, a lx rrnorri BiAHocsrrcs sn k'z.

re)IC

174. 1) 3a Mar. 110.3 LACDT AC'- AD' + CD' = 4' + 32 = 25. B MBct Bc,: Ac, + AB,, BC=J2b+144 =J16s=18 (cM).

r:i*:.:til::li::.:;:t:iil::::

:l:.:ii:i{tiini:.:ljilt::::n: rEOMErPle 6ypaa M.

1.,

TapaceH{oaa H. A.

lii;

763

: 12 + 13 + 3 + 4 = 32 (cM). s^ s.,.,. rs,.,,, , 22 l.a l-1 5 12 6.80=a6 (rM-r. c." = sz. | = 9l r"'r. s," ao I = zr r"*,r.

P,,

A-B

: AE, ao LMPE piBsocropoHEiii, IMPE =' 60". cvMixHrii nuM ZMPL = 120'. AHturoriqso, Bci Iryrl't lllecrrl{yrHl'tKa aopiBElolorL 120" T4_ npaBsnLHr'rii uecrnKyattH&. lcnM trrrsoM. KMPLFH

OcKirb&x An1 =.4?

+ BC + CD + AD

Bianoeiat:

9! cM.24

177-180. PosB'arasH.s qtjx

aM!.

- rprrMoriyrr{rr& s1r napanenorpaM (ZBCI = Zr.{C sli B[yrpinrHi pi3Ho" cropoHHi), y sr(oro AiAroHani pisEi. y LCDB ZCDB = (180' f20') : 2 :30" (ACOD pitsno6eApenqi), 2\ ABCD

rcM). p" = 2(3 + 8.,6)=

oh +

s. "6) t""t. =s.3,6=e\,6

t< --

GM,).

\fi) cu, 6rE cu,.

= 4-D-t =

9!t

Besniq cninEHlrx

cB'

.\B\ DtD cp 48

ToAi 3a reopeMo& osreca A,B, ll AC, D,Ct l) AC, M.Bar A4ACrAr.Dc, Mra r rroeoi(i(HloM

A.B BB. nonrbsocrr !=J=J=t=k.

DD.

176. Ilo6y4yeuo AD i

'{yro

-I-KB. -AKM,1 Tot\1y

ArHfi pe6ep fty64,

A-8c:

2t BCt x DA.B;

A,c,

AD,ll BCc\.

A.BC.

Ha :i'an. 122'. l\ AB e ABC, BC e ABC, AC e ABCi 2l AA, x ABC| BB, x ABC, CC' x ABC, CP x ABCi 3\ A,B, Jl ABC| B1c'llABc; A'c'll ABq PAllABc.

----------------

186. Hi. 187. Hi. gnqo trpsMi, rapanenr,Hi rptMin ll, net(arb y rrou.lrBi o. ro 3a o3Hakorc DapanerbHocri npsMoi i rraoIrrxHrl a lJ cr, rouy rpsMa a He Morrre Mart 3 r o'

Ba.1"E.

1 2

IIIuIIolo

f /\/

/ Ie

\-------7 '.-

\D /

cninl'Enx roqor{

Aore,qeruo qe. lb i a la. To.qi 3a o3narreHHsM napanenr,tsocri DpnMot j !noqxHI, npsMa a napane,rbHa aetltifi

188, Tax.

Hexaii a

45". Bawctr BrnnnBa€, E{o roqxu tI i a cepeqoro B crolo qepry BxflnrBa€, rqo Ko)t(Ha ri cropiH rxecr ftyrHnka

o i FanprkrraA, Aop,unro. ,1222J2

764

BoHa trapanenbHa

185. Tan. npsMi a i 6 MIrMo6ixEi.

= /EMAAK BeprllnanbHi) BHrn Bac. oro AE = A,?

BT = BS i ZT H B \ = ZF SC

npa' nnorlssi, napane"rEsa 'rlcii_Ile6vab i carifi DnorquHj.

1qo

nnoquH , ro

184. [psrycrsMo, Illo npsMa !. Ma€ 3 rnorquHolo c! ABi cninbHi ro'rxn. ToAi 3e axcio_ Morc 3 nptMa a Hane)+( rr, nroqlrHi .l, rro cvnepeqxlE yMoBi. Or)rie, flpsMa He Mo*ce neperlrHarl{ Eroqslly 6inbme, Hitlt B oaniii roqqi.

\r ( KB1 = KAj = A,M = i, 2'

^tK

se nex{slrL y

fl&qo npsMa,

Min

nepepi3 (y6a nnoquHoro, fll.a rpoxoArrb qepes cepelrHu pe6ep,4-4r,

rocrp{M

nepetl'IHamrl'cs, sasxBalorr,c$ napanenb

BC, AB; 2i AZ, KZ, DZ, CZ, BZi

Hexaii p€6po Ky6a aopiBHro€ a. reroM

OsBarca.

'rjcl

"ll"

HeMae cri,'Ir,Htx ro.roK.

OaHa cninblra ro.Ma.

t) AD, DC,

ao'c:I'r M, P,

3 piBsocri rpnlcyrsrKiR KBIT, KA\M 1MA.E

ro.roK.

183, Ha Mar. 121:

tr BiAroBiaso. flpoAo&(trMo BiApi3oR ,\4f Ao iioro [eperrrHy B ro.rnsx I i E 3 rpoAoB)lteHHnM pe6ep BBr i -8.4. qepe3 roqKs E i P trpoBeAeMo rprMy Ao ii repernHy s roqni S s npoaoexnHqrM pedpa BC. Hapeuri npo. Be4eMo nptMlt qepes ro.lRn S i ?. Orpv Ma€Mo llepepis Ky6a y BLIrrrsAi urectut yr'Iv:fa KMPLFH,

ABt

// /"

O3sa'Ie{f,r. flpsMa i rlrorql,IEa, flxi

182.

DC.

AB Ba AD r)A SBiEc' 4181: h Ac, D,q= h AC,'to6'toA,q: - ,rC,. y .rornpr.rKyr'lt ky A\Bp,Dt rporl,ne'IrHi cropoHr.r,4,B, i ,,Cr piriri i rapanenbHi. ToMy A,B,C,r, - naparerorpaM.

-_____________L

ttr--------------

'175. Hexafi ABCD .rorrp xyrHxn, Hs cropoEax sRoro B3sro roqr{ - npocropoBrfi .4,, Br, C, i ,r ra&, rqo

aBox

Mor(nrBi Brrnaaxx:

p"-^=a(r-"6) !=a(t rua) r.rur: s - =g,6.2 =6,13 rcv,r. -"3 Bionolial 4(1+

lpyHry€rhcs Ha 03Haqi napanenbHocri

5 5. B3aeMHe po3MiqeHHt npcMol i nrou{l,rH!l

cr=g=3vE ts30"

3aAac

MMP MP ua:cosl,t' ="- 19 = l.

;l::: fEOMETPI9 6ypaa M. 1., TapaceHxoBa H. A. i:::::*i::a:::i::'#ltii:::::i

npsMifi.Bflnoq{Irict. Toai MaeMo b la i c la, sniaxr D

c (3a osHaKolo

panenlnocri npfMux y npocropi), a ggaqsrl, o3Harcoro raparrenblrocri trpflMoi

i nrorqlllrlj.

D li

i:::ltl:l::tiii::iiliiiiitlir rEoMErPlq Eypaa M.

ra-

a sa

1.,

rapaceHKoBa H. A.

t:::l

765

iliffita

ffi

'f 1) K,P,;

KPi

3' K,Px.

195. He

Boltn Mon lrL 6jrlr MlMo6i,('rnMn.

3dB){c.qx.

196. ArB. l\i

188.

b ll a, B e b, B E tt. tsi^ovo, uro tKnlo nptMa i nlourrrrt Miro,L.rri.rhHv 1n'r-

197. Hexaii d il a, xy, ro

19o. 3a

yMoBoro

ABc,

.toaj,

EF ll cD,

ocKinLF(rr Boslr ne)I{arb B oAHin nro

rrxHi rpaHi CSD i re Morl{yrb reperrrriarnctr, 60 CD e ABC. 3a reopeMoro Oaneca, sKUro t cepeAuEa rS, ro i F cepeAnsa C,s, a ta cepeAHr riHis ACS,

198. 3a reopeMoro,

199, Hexafi a

cM a6o 3 cM;

191. ll DC I AB, AB e d, rcuy DC I a AD i BC neperrHarorb nnoqrlly (I.

oauaxon.

2) Asarori.ruo, -a, I BC, BC . e, \oMy AD I o. AB i ,C neperftHalorB rnoqnFy 3, AB ll CD, C, € (l, roMy .4,8 ll o. ,4, i 8C EeperrHarorb rnourrHy cr.

I AB, AB E d, aofiy DE,,, CrI u3a $xaKoro naparenbHocri Moi i nnou.ltrHr. IHuri aiaroHani neperrrHarcrb nnoqr'rEy 2) Ana"rornruo, AI I BE I cD, rc\4y AJ I cr, r.c ll c. 3, Bianosi1b: cn I a, I a.

1g2. 1) DE ICF

(r.

llp'

il.i!!i:!a:.

,r-:.:r!i:.l.il:

193. 1) Hexaii rpnftyfiiuftn.4BC i,48,

riy cropoHy A-8.

MN I AB, AB E ABD, napanerBHocri rpflMoi 2 3) AEano .rno.

MarorB cnin6cepeaHr JliFir MBC. ToMy toa\ MN ll ABD 3a o3Hariorc

rnorlr{}ri 4,43C. cepcAr{,rn Binnosrallo c€peAEfl ,rirriq 4,4-BC, roMy KN I AB, sne KN e a, rory AB ll ,r sa or"o"u," "opore,'l6Eocrl npEMoi i nnolquHn.

Arr

3pyqEocTi ManloHolr y

O.RinbKx 3a yMoBob ( cropiH -4C i BC, ro n:N

LK1N

LACB- rnn:

1l AB=r::a=18 s\

.na =

16 U11

=zz

(cM); 18=1qr!=16 I

::i:::

nronlrHa,

AaHa

roqlia.

B nxoqflHy 0, naparerrsy

n"ro-

/ e,,/o '"'F

2O0. TaR. [poBeaeMo {epe3 ro'rky,4 npflMy i,], napanetLEy t,, i rptMy br, n8pare,rr,sy nprMiii b. rlepes npsMj ar i 6r, trto Malor; cninL(y rotl{y 3a HrcriL}roM 3 ar{cioM trpoReAeMo

e a, ror'ry a I a.,

rouy

cr.

I a.

qo npoxoAxr! qepe3 pe6pa AAr i CCr. AAPO - nepepi3 ky6a nnonrltHoro, 1) IDoBeaeMo npsMy MN .{epe3 cepcatst M i N pe' 6.p AB i Be. B AA-aC .r4N - ccpenHF riHrr. roMy

2O1.

i S pe6ep,4,D, i CD. npoueaeMo B rpaHi lArr,1) PT D4, .\ B rya4i DD,C,C - Sn | ,D,, roai P? SR P

j nedrarb y AerRiii ntoqlrHi. rpal]6.4,8rC,rr no nptMiii flroqr{Ha TPnS

(cM).

Binoaidb: 18.M, l6 cv, 22 cM.

766

niHit reperaEy i rpera cropoHa nnoulrHa 6yayrL napaner6ri 3a o3Ha(orc'

,uN lAC, oDrie, MN l,a"{,c,c (3a osrranop). 2) Hexan nprMa PS nporonrr! tlcpe3 cepeAxrln

AC M, aB AC KN NC KN. '* KA

(cM);2)

flnorqlrDaT nepernlra€ nroq]'Hl{ s i 0 no napa".len],Hux rpr{_ Mux a, i b,, ane rpaMa Itr npoxoArrl' 'Iepe3 ro.tlry B. a nptMa It rano)n neniur! y nronrrHi Y, npoxo4lrrl qepes ro'rky B i na_ pana,rbHa rpnMifi ai. To^i sa a{cioMoro napa.'Ien6Hux npsMH)t b i b1 Maroib 36irarncr, roMy np'Ma t te,Irxrb y nnolrl'iri [].

b lbt, ble

'194. 3a yMosoro nnorqr{Ea d naperliEae nroqnry 'rpERy'r!'xRa iBC no npsMin ,(N. Po3MsseMo

AaEa

qepes roqky Hexaii b - AoBinlla np.aMa, s]{a npoxoAxrb B i Fapanp,rbHa d. Bi3bMeMo B nronrrHi cr AoBirbFy roqlcy A i npoBeAeMo qepeg ro'rEyA i IIptMy b rlnonlllEyT.

a I a,, a,

nrolliuHrr.

B3aeMxoro por'r:t-

o6epHeEolo Ao reopeMlr oa,'leca,

IpoBeAeMo qepe3 roqy rlrrEi d.

2) 1,5 cM a6o 3.5 cM: 3) I cM a6o 2,5 cM.

Bl{rlsal{ ix

napanenbrri, a 3Haqrrb, cropoHa

EF = !cD.

1) 2

Mo)rc"rnBi nuIIIe rBa

uyBaHHr: nptMa neppr Rac nnour Hy i npflMa nexurb y rnorqr.rHi. 11 npnnycrxMo. uro nptMa b Hp nexnrL y n,lourxHi e, lr ne perrrHa€ ii B roqqi B. ToAi B,rxoAtrrl', qo oAEa 3 napa ,renr,Hnx npeMhx .1 i b napa,renLua nnoLlruHi a, a trpyra neperrHa€ qm nnorqxHy. Aie lre rBep4(eltHs cyflepeqr'T6 AoBeaeHoMy B 3aAa'ri M 188 onopHoMy Oaxry. Orrie, saule npx yqeHHn llenpaB1r,'lblle, rpt{Ma, nenitrr6 y rnorqxlri d.

rEOMETPI9 Eypaa M. t,, TapaceHxoBa H. A, r::J:::::::::iii:l:!:iltti;:::::::i

'eperuHa€ PR. BiJlpi3oF PR napnn.rbHnii A,C, flK

r.pcnH',riHis

,\Arr,Cr 3a no6yaoBoro. Toai PR I A,{IC,C. AHa'noni.t uo | ,4.4,c,c. "s Ea, qo npoxoAriT Ilnonrt

b qepea

npfMi

P-R

i ?S,

He Ma€

A 3Ha.rurb, i npsMs PS, qo in Haner(r{tB, or}lie, Ps ll.4/,c,.

AArC,C.

r::::::::::iii:ii:iijaii;:i:.:..:.':i

rEoMErPle Eypaa M.

1.,

cnirlrH!.tx ro'ro1l

Be Mac

nnorql]Ilolo

rardrx roaroK.

rapaceBKoBa H. A.

l::::r 767

MoJr(Ea npoB€cr]t Bi,qpisolc -il4N 11.4'8, roAi BiH 6vAe ByAb-sr(rtfi BiApisorc y tparl,i ZAB' Ilnpa.nenb rft pe6-

202, .

napat€nbHsii rroqrHi -4Bc'

BiApison trpoBecrl Ee Mo]i{Ea

BtuLMeMo lra

203. llj npsraj norpL6Ho trpoBc.rr-r noMy 6iq]ioMy pe6py qrx rparei Eocri npsMrx).

qo flIlulo flpsMa, sKa ne fipoxoatrTl' qepe3 BeplltrEy rpnKyTEr'IRa' trepellIsa€ oalry 3 ioro cropis, ro BoFa reperlrsa€ rit6lcr oAsy 3 aBox iEErx cropiE'

2O5, AsB. l,l! 191, 192.

206. Hexaii d - 4alra npsMa ga a(cioMoro Hare, iEocri rocoR i nptMlrx Bbr'MeMo roqlry -4, alca Eanel*irrb rpsMin a, i ro'rRy B, rqo ii 11e Eane'rrlrr" Ba EacriAKoM 3 3 aricioM crepeo_ tlepes ro.rn{ .4 i B trpoxo4l{rr, €a{Ira rpsMa '43' 6e3ni'r nnorqnr, xo*cHa

rrp"*y,i'e rpoxoalrrr,

""pee MyaBtoqqiA. 2O-L

IJexail d

Dp€My a napanenblro Eanexsocri ro.roK i

ABi AaEi

slotx reper{ua€ flpn-

arca npoxoAgrb qepes qr'oro BisI'MeMo Ha npEMii d ro'r&yA (aRcioMa

rpsMi. IIo6yAv€Mo IInoq'IHv,

trpsMifi ,. Ars !Ip.sMltx),

rpoBeAeMo qepe3 trei EptMy

Miii b. IIpoBe,4eMo .rep$ trpsMi d

01,

napa"'1enr'Ey

IIp.rMa

,lj

D trapa,'IerEEa

rpfl-

'1' o (Irac'i4ox qo neperfilramrbcs, trnolllljEv

2 3 aKcioM crepeoMerpii).

ri:

rlpsMii br, rqo JIe}I{l'Irr' y nnoqlrHi c[, ror"rv

cr aa oanaven"

60 aBi rpsMi, npoBeaeHi 'repe3 ro'rllv A, B3srv na npsMii a' trapa' 3 npsnen6Ei AloM iIrLEnM AaE rM llpsMrrM' He 0608'n3fioBo ne)<arb B onsiii rlJloq}llri

2) He saB)riar,

.i: ii ;,i!:;1{.t:.:t.:i':

lif:!*li:if: fii:tii'ii*i iir'l:

f:::l:i:.ii

rpaHl' ABS aoBinbHoi nipaMi4 3 BepulvrHolo S Hexaii A1 i -B1 BiAtroBiAEo cepeA,lns 6iclrtlY pe6€p '4,S i BS' ,'linig rpslyrE fta,43s, roaiArB' ll'43, i A,B, - cepe,qHg orr.e, A,\ | ABC.

208. Porrrsnemo

AEanori.rEo, Biapiso(, satrp,rKnaa, -4rrr - cepeaEs nisifl rpnKyrsuKa ASD. ae AD_ o.nHa r 4iaroHanefi

rouv A,r, I AD,

209.

1) Tali; 2\

o1r'ae,

4D1l

ro'r-

rprMiil,4,B i4my AoBitbBy ro.rHy N i rpo-

BeAeMo qepes

nspanenbso coi'16 (o3saria napanenl'-

2O4. Hi. AaHa lnoqllsa reperlrHa€ flnorqlltrv rprnvrEn]{a I1o rpnMii A 3 i{vpcy nnaEiMerpii BiAoMo'

BisEMeMo Ea npnMiii -4-B AoBinr,Ev

3a HacniA(oM 3 axcioM crepeoMerpii qepe3 trp.sMi a i -43, rqo neperrrHaroaLcs, Moli{Ha [poBecTl,r ear'IHy nnoIIIlI-

pr AZ,6y1e sapanenLE:,I1{ Il.not\trEi ZA'l' Ao peutrl, nnoquH y Eroq Hi ZAB napar\entsau&

*.ipii

210, Hexei.43 i CD - ABi MriMo6ixEi rpsMi t{y .'tr/ i rpoBeaeMo .repea nei npauy a ll Cl.

Eei npnMy b ll CD. 3a ossalroo naparemHocri npsMrrx a I D, a otxe, BoHLI Bnsuar{aort ealrny trnorqrHy l]1. Asi roqxr M i N npsMoi.4-B nelnarE y rlrro' qllsi q, roMy.4-8 e c[r, a qe ooHarrae, qo nnoqt{sl, d i clr 36irarorEcs. Orrre, Bci rprlMi, n&i neperlrEarcrb.4.B i napa"re,'rbHi Cr, neniarL y nnonlltHi Cl. PosfnsHeMo slti-He6yAl, ABi AiaroHani rapanenenineAa, nanptrxnaA' AC1 OcxinbKr.r .rorliplr1ryrlrnl""tt ABCD i BB,CTC - rapsnenorpaMr-r si cninrHolo cropoEoro BC, ro ix cropoEr A, i A Cr _TapanenbHi, a 3Haarxrb. nerrar6 B onuifi nno-

211.

qlrlli i

trapanepiBHi. ToMy .{orriplrltyrllrK , rrcr, rorpaM (ABi npornnex{si cropoHE piBsi i rspare.'1Elri). JliaroHaniACr i 8rD ndpancnenineAa t triaroHa,lflM}j a6o ro napa-rerorpava. ToMy soHu neppT Ha$rbc't i rorKolo neper Hy O Ainfll hcq saBnin. AEanori.rEo aoBoAnMo, rlo aiaroHa-Ii ACr i Br) ra aiaroHari AC, i a4 | nFperudalor6cs i ro'{Korc nepel r.rHy Ainerb_ cs HaBni,q. 3siArl{ Bx.HoBoK: yci vorxpH aiaroHa-ri Ea , pa.ne,renineAa nepersHalorEcfi B oAsii roqqi i ToqRolo treperlHy Ainnr6c.f, EaBnin.

i,Br.

212. H1xait AAI-D - npocropoBlrn qorxpxx) rH/ri- i nnouuHa 6ir*{snM IlpsMtM ,4'B i Cr. Ocxi,rxu ,4.B ll cr, ro rnorqElra q He Ma€ 3 npnMoro .4-B onirr,Hnx ro.roK, BHa.rLIrb, fipfiMi, no sxlrx trno]]l]rEa

naparrerEr{a MnMo-

q tr€perrHa€ rrnorqdrlr rploi ro.roE l-BC i /-Br, rlapa' nerLsi Eoro

-,4,8:

PN I ,48,

ll,4B. Toai

-&M 3a o3Ha'

[aparerbsocri npaMr'Ix.

I3 napsne,lEsocri nnoE{Esrr or i np.sMoi C, 3En''IlIBae, qo i nnoqlrlru,4C, i BC, neperrEalorb nnorqr4By a no D napanenbHrrx trpsMtrx -KP i MN. napajeiorpaM TaRrrM qrHoM, KPNM

3 trapanenr,Eocri

ABC.

nEnBa€, rqo

BiApiBKiB

MKP -

j. DC M MN i DC E$' i AMBN - IrBC, roMy:

I(P

LADC

AK KP MB MN AD= DCt DB- Dc

'li.s

A-'leI(P: MN fl1l nporsnernHi cropoEt, napaie"toryaMa, AI( MB Ha c( cropollrl ro6ro nnoqv ,.*y air|rl' 6=;, .rornpE1{yrHrIfta /,8CD i BC rpocropoBoro qiini BinpbRlr.

?13. TprKyrHfiKn AB. i ADE Malorb .ninbsy BeplxxHy A. DEI B(.3a orFatsoo oapane,rbHocli nptvoi i nnorqugs, ocri,rffiu DE I BC, a Bc c ABc, ro DE I ABc.

768

li{: rEoMErPle EypAa M.

-4,

Ea npotrop

1.,

rapaceH(oEa H. a'

iilttllfiilltlllliil:::i

;ri::i:jlltili;i;lii::i;:it:il! rEoMErPlt Eypsa M.

1.,

rapaceHKoBa H. A.

l!:l

769

qe npsMa' Brna.qxy niEis reperulry rnoq!{Il rprlrrrHr'IKiB '4-BC i A" qo rpoxoa[rr' qepes ror{&y -4' rapanenLna rDsMIrM EC i qepe3 roq$v-4, 60 3a aKcioMolo 4' nriu{o ABi rno' ", ,4oBeAeMo qe. IIpEMa d npoxoAtrr, trepert HarofEct ro trpnMiii' ulo npoxoarrr) Bolru ro roqxy, crrirlLEy rrtrrHr{ Malorb qepe3 qlo rorrKy. rE, 60 B iH oMv Bsra,q1rv rpsMi a i DE Malorb cdnbHv npgtu o ttap-","ot a "psMin ro'rlry 3 trnoqlrHolo A-BC' qo cyrepe'rrrr' vMoeictrin6ny ,,0 Mae ro.rRy, i npnMa

y ra(oMy

6. B3aeMHe po3MiuleHHc ABox n'loult

nroq'lrlr

ABi piasi

qii npnMii

,'rerriarL

Burarru

D C[

223, 1\ ct IABCDi 2, 3) 9 I AA,B,B; P I CDD,C,.

6vrl'

reper{Irarrct ro npnMii. Ha yci crli,!6si roql(r Aasnx IIno_

224. 1) ABCI Appl'60AB x BC' AB lA'B" BCI B'C'i 2\ ABBII DCCI60 AB xAAI, AB DC, AA,I] DD; 3) B,c,c l) D,DA, 60 BC x cc b BC I AD, cc, I DD,.

BnacrxBocri 1. .gllruo qepe3 Ror{Hy s aBox naparenr'Htx rlps_ MIrx rDoBeAeHa nnoql{Ea, rpsqoMy qi EroqrHt trepernEalorl'cs, ?o niHin ix nepertrHy raparerbHa I(oxrliiii i3 .4aHlrx npsMnx. a e cr, b € P, a Ib, rowv a lc, b\ c.

225. Hi. Ta$\ niour'1H14 \rolr{ylb neperhrrarr.r no npqvii. naparenbHiii aaHuv fl peMt{M.

226. Hi, ri,l6r(/ \

2. glcqo npsMa rapanenEFa RoxrHiii 3 ABox rL'IoqrH, qo reperr.tHarorbcs, ro BoHa trapa,'IenBEa rpfl_ Mii ix repeflrHy.

BMoaAr(y, sKuro

nprMi,

227. Iar",

trr".'lq]

npsMi Mr.IMo6

{Iri.

22A. n^oll.^vh o i U nFperfiHarcrL.rr no nprMiii 4,8,

3. flErro n,lorqrrHa npoxoA1,lr6 qepes aaHv

npe_

229.

AsHiii rpsMiii.

23O. l) OaEv (o.HoBHa B,raerLIBi.rb). 2) Oasy.

217. 1) IlnolqlrHlr -A-BJ, i .4-BC nepertrranrBc'r ro npsMiii '43' slia n4panerlLHa rps-

AP-\

DC.

3) n,']orqnEI-r

BCC1

t ABB1 neper"EaroTbca

Crr,

ttptt[Lrt

IIapanenBEi nron({trx ABi

rroqt{Iln, al(i

IIe repeaIrHaIol Lc'i' Ha3uaalorlca

npq {i. rn 'r' p.-r ts rrorb'fl. oaHi' i nnoqxHlt BiAnoBiAEo napanerLHi nBoM npsMrM Apvroi n,rorr(uqv, ro ur nJrlouLriHrr ndp,11'ibH' OcHoEna Bnacr{Bicrr,. qepe3 roql{y' nEa Fe te)(Irrb

O3uaAa.

AAr.'Ra napanenlqa npn'

I]epernHalorrcfl ro flpsMiii cC,' flEa rapa-trerbHa rpsMI{M

DDt t BB\.

fsulo As'

y nnoqr,lrd, Mo8sa npoBuclu nnor4lrHv' napanenLr{y

AaHiii nnorqs:'i, i rinl'Rtr

oAHY-

N f=

--l

lr.<I:!

AgP' AB I A,-B,, Bc ll B,c,; AA,B, IDD\(,M I DD,-AtB Dt l /-A\D I BB a . AA, BB.. A,D I R. . 22O. alF,a\tl'. 218. ABC

221.

Ta1r,

v qroMy slinaAltv niEis neperl{Hv uorqlrn

napaten6Ha AaEiil rp.tMiii.

77o liii rEoMETPlc

He MorIlEa.

napa-rerbEin

6ypAa M. l', rapacenroea H. A. i-:'.-!.:l!ilii::tiiiiiiil:l:l:l:ii

r e AB la(c

ova 4,.

IInolIqEa napa,lerlorpaMa Monie teper}rEarl{ nnoqally o no rpsMifi,

My, napanen6Ey iHrxiii nnourtl.Ii, i neperrHae qm rnolllr{Hv, ro nillis reperlrirv tuIoIIIrJ]r napanenLEa

2\ nnoirysu 44D Mv\ DDt BBt

u1o np}l{arir B oa-

Hiii nnoqaHi, [eDersEaror6cs.

oll o, alP, mmyalc

L\AM

allanori.rlli.

B npocropj Mon{vrr' a6o

trapanenEHrMn, a6o

222- l) CDl.4J sK rporr.rneniEi cropolls naparelolpaMa.

qr.rM cropoHaM

napajrerorpaMa

231. Hexan trnoql,ll { cr i 0 neperuuantr,cn. flx6rl tnorquEa Y He repertrEana J{roAIry strrorqlrHttiB,rornourrHr([iB6ynr6rapa-re,'rbEinnonllrHiY,a3Ha.]rrb,iMi]{

co6om,

qo cyrepeqrr!

moqug c i

yMoBi saaaqi, Orlre, nroqIlr]a y neperuna€ xoqa 6 oAny i3

np.flMa a napanerlna nnoq'Iri (l i neperruae rlnorquny p n rovui B. 3 oBEaqeHHs napare,'rbnocri np.nMoi i nnorqnEr. B1r' nnaBa€, qo B n,'Ioqrlri c. icHye Aesna rpsMa 41,

232. Hexan

DapanenbHa

rpnMin d.

n,roulHHa, rHa npoxor/16 qepp3 napalerbHi npeMi a i a,, reperuEa€ trJloqrry I ro np'IMin b, sKa rpoxoAnrb rrepe3 rorrBy B (a(cioMa 4). y qin nnoqrHi, ocninl,nn npnMa B treperlrna€ oAHy J apaie"'rLsr.x npsMxx d, ro BoHa nFperuFac rapyrY or. TarirM qr{HoM, np.tMa tr,, a sxaqrlr!, i nnoqllHa o Ma€ crdnlEy roqxy B nnonrlrHoro B, ocxi"rrxr b € B. 3a aHcioMoro nnonlnHu Cr i 0 Maror6 cni,'lEHy roqKy, ro BoHLI reperl'rHalor6cs.

4, ocRirbKfi

napa,'renbEi rno]]]xHr{, A € s. B sa,qa.ri d 199 6yro AoBeAeHo, Iqo 3ci np.nMi, Eni trpoloAsrE qepe3 rorrliy -4 napanenr,Ho nnoqmri [:], rer{arb B oaFin r,'ronrnHi. Ilo3Haq'Mo ii cr,. ToAi .repe3 roqriy,4 trpoxoaEr6 ABi rnoqrrHr.r cr i or, napanerGErx nroqrni L a"re qe HeMolrinrBo 3a ocEolHo1o BnacrsBicrlo napajlenbHtx finorqltE.

233. Hexan o i []

:ii:{iifiiiiltaai:jiatii rEoMErPle 25*

EypAa M. 1., rapaceHKoBa H. A.

liti

771

tl€pe3 roqKy OTxte, rlnoq,Ilta crr 36ira€TLcs 3 fi,toqssoro s, i fipsMi, Iqo npoxoAfirs nroqrHi o. r€l*iarb $roqslli A napanenEEo v B,

2) AA\B I CCI, 60 AA, i treperrHarorLctl, ,to "trB1

flrorqrHa 0 rapane,"sa i rJloqlrEi cr, i rlnoqrl{i Y' i 1 Malorb AesRy clrirlLlry roq(y .ll1 ToAi 'repe3 ro'rKy ]ly' npoxoAsrl' ABi r,'Ioqlllitj cr i Y, lapa,'Ienl'lii nnoqlIHi B' nlo HeMoxnl'rEo 3a ocHoBHoIo BnacrtrBicrro rlap rerbllltx trnoqlrll.

q AACIICC.M (M

234.

SaAa.ra onopHa. 3a yMoBoro Her(aii trpa q6oMy rnoqtrllr ct

cr i F lle Mor{yrL neperssarIlcs fl1r6u rlnoiqrlllt C[ i ll Manlr crinbllv rrepe3 qm ro.Itiy trpoxoarnn 6 ,qBi rnoqlrlrr (s i p)' apanerlLHi nnoquHi Y ro rorrfty, A qe cyrepeqtrB ocHoBliiii B,'IacrtBocri flapa-lenbHld nnoq {'

235. Il.noqrmr

236. He o6o!'.tsKoBo. Il'Iorqlrl]s a i

0 Mo*cyfi' repervHartrca

AACP trapane,'lorpaM, ocRint'xu AA, lCC, i AA,: CC, sR 6iql'l pe6pa xv6e '

237,

qrstr.43,C rapa'nenblri ABoM urlrHu A'r''D, ro lli nrolqrHfl

npnMt{M

C,, iAlC,

ltpoBetreMo lrepF3

slii fleperlrHarorr,cs. lIa

1) IlnoqsHa

-43rrt reperirHae rpani

rpaEeii

n -j

ocnoBi osHaKE ]Iapa-rlenEHocri ABox nrorquH

MsMo6ilKId).

Orlie, napa raparent'El{x n,'lorrlljH

€AnEa.

239. Hexan 4 ih -AaHi vrvo6i)'{Hi rpnMi.

r{epes aoBinr,lry ro'rRy rpsMoi o npoBeaeMo rpsMv b!' napa_ nenbEy b, a .repes AoBinLHy roql(v trpsMoi b f,poBeAeMo Irpn_ My .l1, Irapanenbgy d llpoBeaeMo.ABi rlnorqLlrrI: oaHv q€pe3 rpsMi d i rr, a apvry - qepes trpsMi b i ar' 3a o3lrar{olo fla ps,lenbHocri n,roqsu ui aai niourxHlr nrpa.rF,r'Hi'

24O. 1\ AAP. I DD'F', 60 npsMi -44, AA.1 FF,, ,ql F,4.

772

l::1:

rEoMErPle sypAa M.

CF4 repernnalorbcfl'

1., rapaceHKoBa H.

i,4rr

(rcor(Ea

/=7 -2,

l-41

3 r{yooM ne}nur}, npsMoxyrHrr{ ATBCTI nepepisoM xy6a nnorqsEoro B,B, e np.sMoRyrs K aa,D,D. ix n,rou:Hsr valor6 asi cni,16di roqrr B i rr, roMy nnoqlrHq.4rBC c1 i BrB, repernHarorr,cn ro npnMin Br1.

fiprtrycrrMo, rqo .repe3 rpsMi.4.B i C, MoncEa npoBecrl qe oAEv rapy napanenEH,rx rrlorllrE, IIanpn(JIa,4, .4-BA, i CDCr. ToAi BItxoAI'Irb' nlo trpsMa _43 rapajlentHa rrrorqnsaM CDq i. CDC, i tdsii ix neperuHv rpnMin C', Il{o cvrepeql{rb

i C,

Ry6a no BiApi3ltax .4-BF BrDr

Mae B

A-B\I

yMoBi @psMi,4,B

BianoBiaHo

'rs va( 6tar napa-nei6HaniHii irepersHy aaHlrx finoq&s, Tafi}lx llnorqnH Moj{{Ira fipoBecrfi cepea: 1) ro.rEy -. 6eaniq; 2) rpsMy, nRa rapa"{enbHa AaEr{M nnorqnEaM,

i C,C1. /

naplr trpsMlIx, (DC I

riEii

IIoBiAso B roqRax M i N. IIe cnirBlli ro.{lia AaIIrx n,rorqr.rH, BHarrrrr!, nnoqlr]l'v A-B p I i A\BD neperlrrraroTl,cs ro rpsMiii ,Mlr' (aKcioMa 4). 2) Y repersHi nnoquH, A.BC

ro.Iny -4 rpnMy .4'4r, raparenbHv rpsMiii C,. Altanori.rEo.rep$ roqfty C npoBeaeMo rpsMy CCr, rapanenL_ icHyrorr,, 60 BoIrI{ rpoBoAtrbca qepe3

cepeaHi

ci.$oro flnorlfirolo aBi cninlEi roqr<l,r, a 3qaq]il6. BoBr ncpprHpa|orhcE no npflM:;. ulo npoxonxrb 'repe3 qi ro.rRu). AHanoriqEo, nnorqrrHa .4,8, reperr.rEa€ rpaEi lty6a no BiApi3rca"x -4,,B, B, i -4,r.

nj,outal'/ BDA.. ro ui nnoul Hx napare,rbHj.

,4-8. PoBInsHeMo trnolllutlr,l ABA1

crin6Ea roql{a.

242. Tan. MorftHa. E,roq

3 TpEox

A\BID - raparenorpaM, ocliirLt(r 4,Br ll CD A A, a, sx trporruexE; pe6pa Ky6a. Toni A D ll A,C. a,,b,ie - nap-"ro.pav. 60.A,D, I Bc i A,D BcIoal, A,B ll DP. OcnirLEr ABi npsMi B1C i D,C, Iqo treperltHarort'cs, ' A trnoqnrlr B1r1C rapanen6lii ABoM npsMnM Ar, i,418

rpsMii

241. 1, .BCD I KMN,60 KN x KM, KN ) BD, KM I BC ak MBD ] AABA. 2) AtsD ll LME,60 Ats x BD, LM I ats i LE BD $'. cepeaEi nilrii 4,4.BC i A-B,C. 3) AcD I KLF,60 AD x Ac i KL ll AC, KF ll AD aK cepeAHi niEii d,43C i d,4-BD.

243.

i,4

IIi rndqrsII

A1^ | F,q.

nno-

FFb

3) rpsMy, slta trapanerbHi oAHifi is trrTor{rrl, r*{oAHoi; 4) rlpaMy, slca n€perqHa€ AaHi nroqlrlr, oAny; 5) rpaMy, slra netlrlr6 B oAEii i3 Aassx rnoqr.rH, 6eani.{, .sKs{o 4n npnMa naponenbHa niHii neperxHv nnoruun, iHaxule }l{oaHoi.

napa-ne"rbHi

238. Hexai nppvi A-B iCDMI'{Mo6ixHi

cep€a'Ea -4,8), 60

6e3niq;

roai ec ii.a,c,. AxaroriqFo, -4BrCr, - rapsrenonpaM' 60 B,ql AD j, BPt : AD. ToAi,4-8, I c,D. OcKirLxLI ABi npsMi -431 i 2tC, qo trepersEarorbcs' rno-

AAt

3) AB,CIDEI, 60 AB\ttE,r.

3) I]epepis riy6a rnoqnHom.4,rjc

{BCD|.

ABp

np.sMoxyrnrx

ITepepis xy6a n.rrorlrnorc

np.EMolryrllun-4-BrCrr. To.rRn M i N crdnr,Ili roqltla nnorqr:d {Dp i A-81D, roMy qi nnorqlrnu neperr{Haor6c.B no rpsMifr MN (aKcioMa 4),

244. Mo)r(,'ln3i 1ci"!E&a Brna.qrdB. l) gnuro lpnnyrHrEx ABC t BCD Marclb He rinbKx crinbHy Bepursy C, a fi cninblly cropoHy BC (a6o ir ry), roAi caMe npsMa EC i € niHi€ro neperrHy nnorqrH rpsKyrHrrlliB.

ii;:llltiiii:jiill:.:il:ilii

i:iiiitlilillllJllli:.:',:'* rEoMErPle Eypaa M.

1.,

rapaceHKoBa H.A.

itt

773

251.

2) Tp{riyrEnriq Maloab crrirbHv B€plll,triv C' SEaiiaeMo Apyry cflinbHv I'o'rllv trnoslnll ABC i CrE. Arn rrboro trpoAoEEEMo BiapisKE AB i ,-E ruvRaHa trpsMa' ao neperlrny B ro'rqi O. OC

1) .flIcqo ABi rnoqlrl{r rapanenr,Ei, ro rpers treperrHa€ ix no napanenb-

2) gKrro rnoqrur tortapHo neperrI sarorbc.a, ro niEii neperrHy Mo?nyrL

6yrr

naparenbHr.rMr.I a6o reperllHarr.rc.{ B oaEiri roqqi.

3) .flHnro .48 I ,t, ro trpnMa nepertHy rnorlr.rH flpoxoA rr, qepe3

napanenBso i ,E (.fllrlqo qepe3 nolnEv 3 ABox raparenbH{x npflvux npoBeaeHa nJrouxHa. np o1{y ui nnol'rl,lnx neppr ri rls rorb.t, ro ]x niHis nFperrHy napajlenbna Ko)lrHifi

10.r&y

npnMnM r4-B

ir aanlrx

trP-tMsx).

245. JIiEii reperrEy z',, d,, .r3, ... rapater6l{r' ffpo*a o .rupu,""rro"u Eoifisifi i3 trpsMEx a1, 02' a3' -,60 illallrre AaIri trnoqrEl crinbEi ro'rRI'I! rqo cynepeqrrl' vMoBi: nroqlrl r rapanenE ' 3a o3lrarcm raparenr'trocri rlpsMIjx y rpocropi ABi rpsMi' napatenLlii

Ma-!II 6

rperifi'

panenlni Mi}r{ co6orc' or*ce, o' I o, ll a. | ...

246. Hexail a i -4

253.

npnMi BislMeMo 3 rpocropi aoBinbsv roq(v b - Ar'l Daparenr'Hi qepe3 i npEMy a nroql'lry o r{epe3 trpnMy t npoBeAeMo

rpoBeAeMo

ro'rKv A

nnoqlr]Iy, rapane,rbtrv

lx.

ro i rap naOcniarrcn roqxy A sa aKcioMolo 1 Monrra BI'I6parq 6e3niqqlo cnoco6iB,' napanej1bHi rlp-tMi a i Mot(Ha EpoBecrr'I be3jlr'r' panenb{Lrx rnorqIIII 'Iepe3

247. ALs. }.!i

:,i ll:i

n qepes roqxv M npsuv b' I o' ' ""o.q""i qe3a ocsoBHolo Bracr[Bicrlo fiaparenbHxx fipsMlrx npsMv' oaHv ri,'l]']{r trpoBecru MoxiEa pe3 roqRy M rapare"'r6Ey IIPsMiiA d. Ort(e, npsMi b i 6, 36iralorbc.3, roAi b € c!'

rpcrl,oro ro opnMi nepcll,,t') , a_

2. fiKri{o ABi npsMi, qo npperxEaorhct. sinnoBiaHo napa"lenEHi aBoM iHj.!rv npsMnM, rqo neperr{salorBcs, ro Kyr Mirrc neplnuMt npnMEM AopiBHro€ nvrv

,Ci.iIIa rnoqnHa .4,{,r'D neperuxae AaHi rnorqrlil. no trapanenbHrx npsMr'Ix AD

Ap, ci,r]f,a. AA14 ro rDnMnx -4'B ,4,-B1, ci'rEe nnoqrEa BBTC1C tro trpsMl'Ix BC B,C, i. ci.cj:f,a DD.C, - ro rpsMrx ,C I D'C1. ycLoro ci'rErx nnorllll{ tr'srr,. Ha Mai1. 148 rpr ciqHi rrotrIuEn: ,4BS r€perlrHa€ rnoqllHv -4JC no nprMiii -4-8, Bcs nepersHa€ nnoqrHv,4-BC ro nnorqrEy -4,8,c, - no trp.tMiii,4rBr; unoqsHa npnMiii BC, nroqrllyArBlCr Do npflMin BlCr; nnorqltHa -4CS reperlrHa€ nnoqrL

3a o3Ha.re1{lifiM.

2) Tpx 6iqHi paRr pr43l!1u rlapane,rbHx {u 6v1/ He Mo 60 He icEy€ Mlrorollvrtr]tKa 3 rpr'oMa raparenr''Icyrb, HnMIr cropolraMr'r.

Ev ABC i \Bp' BianoBiaHo no npsMfix AC i A,C,. Ha Man. 149 ciqsux rnon{rE qornps: -4-4rB,B, niEii neperltEv

,liHii trepeflrEy BC i BlCi DDpp, niEii treperssy

fieperlrHy-,4,i-4rr,. 254.

3a Man. r41-t AB x BC

to!'i - ABe .AtBC. 3a M;n. 148t AB x Bc, rcaj. /ABC : 1A1BP\.

ABCDEA$$pP|

rpflMa np!3Ma' B ocEoBi nloi ne,Icl'rl' npaBlrnl,E{ii r'flrl'IKvrsuli'

25O. ld.exaft

1. .fHUlo ABi napanen6Hi o"qotirHHr neperHyrlr panenbHi.

256. Ha Man. 14? ci.rHoro e rnoqurla NMMr, Bolra neperlrHae rnoq\4 sv -43C no rlpnN$1. Min NM, rnorqDHy.4,B,C1 - no npsMin Nr A'Ir NM I

"Jai::::::: 6iqHi rpaHi' iti::-.,r::l 249, 1) Mot<yrb se 3aBr{air. Hanprxna{, napa-renbElrMrt Mor{yrE 6yrlt sliEo naparenbHi BiAroBiAEi iM pe6pa ocHoBlr' 60 6i'{Ei pe6pa flps3M raprienb-

l{i

7. BnacrllBocri napanerLHxx nnou.lltH

3..qBj npnvi. napanen6Hi tr.pneH4rH)ntpHlIM npnMxM. nepneHAxKvnflDHj.

irpo"u,q"*o

ji!i:l-l.i'i.|.::::i

ITapanenEni.

'Milr. apyrsMn.

199.

248. Hexaii rpsMa a raparrenbHa Ilnoqrtsr cr' Bfu6MeMo B nnoqnHi {r ro'iKv '\4 i rpoBeAeMo 'rep€3 Hei flpsMy b I o- AoseneMo' Irlo npaua B nexnrr "iu.lt:.::,,':: t;1.;r.3t::.1lrn

252. 36irarcrbcn, leperrlramrbcs.

BaMar.1,4gt AB x BC,

B, ><

A\4 x BPt : 4, AB I A,B',

1A\B;

BB$$'

-,4-B i Cp'; AAQP,

.nL]dI\

BC I B'c',

Bpt: 4, AB | 4Br Bc B\Cr

AEtx Bp, AB lA'B',

BC I BtC,'toM.v ZABC =

1A\BP|

IlpoBeAeMo AiaroHaili -4, i -4,r, ocHoB. Toai nnoqsna, 4,rr napatenBHa flnoql'IHi rpaEi BB,C,C

3a reopeMoro npo tapanenbAi rrolqrHl i ciqHy rnorqzsv, ocltir6xr'I ocHoBr-l npr.rryr napane"'ilHi. ro ciqFa nrourvHa Ma. neper tsarr Ix no napanenbHrrx

rprsMlr' A,rL I Blcr (a6o,4, ll Bc) sx ocHoBIr piBHo6i'nroi rpa-

npsMr.rx. Tar{lIM qnEoM, ci.rfla nnolllu Ea Il€ Mor{e [epernHarlr BepxEro ocEoBy trpfi3Ml' no rp.nMnx, slri se napanenBlri /,8.

.4-4,

lBB,

r.er\ii

724

f,K 6iqHi Pe6Pa

48P'Dr

il:i:rEoMETPlg EypAa M.

1., TapaceHKoEa

H' A. itlili:iilf:lilii::::r.:.:di*

ltli:;:{iiiiifiii:lfiiit

rEoMErPle Eypaa M. l', rapaceHKoBa

H. A.

itt

775

260. Ha

Ma-r. 15Ot

264. 1) IInoqrHa Prtr'

LM, PL, QM.

Ha Ma"!. 151: MD, CL, NK. Ha Ma,. 152: PR, Qn.

Hrcx

nep€rr.rEa€ napanenbEi rnoquss ABC i A,B,C, no nrpaneninpsMrx PN i MK, aHanori.{Eo PI( ll MN. Or,$e, D

KPNM

napanenorpaM.

3a )Moso'o ciqHa n,rourrrH. naparerbHa tpaqi AA-D\D. 261-

orl/!e,

iilF ttl

AAP.

K PN.

flnoIlIHHs ,4-8rC_ neperftHac ,I napanenhHi nnoulH Hr.r no napanenbnfix npsMl{x A,D] i PN, a nnoq,Illa

\,,

iri irl

^',

/,",

t,/

_ 't',1 'iri /

l) nnoqura MNP(

2) flnonrrHa

rIeperrrEa€ napanenh

rrna€ napanenbIIi

Hi nnoE{'ar ,4-4rBL i DD,CL ro npsM'rx MN i PKt lvIN ))PK. 262, AtsCD t A,Bppb r\ AB I c,D,;

,,l

ataP.u

Dno-

3) Ilnoqulla PRsr fleperrrHae napanetrHi nnoquHr

ABC 14BP\ ro

A,BC i.4,B,Cr no trptMtrx RS

QrT repe-

i P?: xs I Pr.

rpsMlrx 8,L i iaF: QLl KF,

AA!,B I Dr,c,c,

MKi

AA,l PK, A,D,)l PN, A |o(i ZKPN - 1AA1D\ = 9O". TaxHM qrHoM, -KI'NM - rpaMo(yrHrr{, 2) O6lpysry;asrs aHanori'rEe 1). poKPNM - EBaApar, 60 PN - 4D| KP - AAt $r! rnne)nEi croposB rapanenorpaMis 4DNP \ A4PK Bi4noBiAHo.

265. l, finour{ira-4Alrr Hxx rpnMr.rx

n€perrHu€ naparenl,H:, nlIon\vHtr ABC iA,ArCx ro napa-rerb' EiqEi pe6pa nDaal',rBnoi rprr3Mr-r ct DD,, roni AA,D,D napanenorpaM,

.4, i Arrz.

trapanenbEi: AA,

AzD'

iHlni rpaDi npr.r3M'a Henaparrer6Hi.

2) NP

AD.

Araroriqrlo, p$rnssyBrrr neperrrg ci.{Hoi nnoqrlgx uruMu 5iqHrlMH rpaHrMrr npnJMrr, orprMa.l'ol A,B! AB, A,B, = AB: B,c,l BC, B,c, = Bc; c"D") cD, c,D": cD. ABCD xlaApar. 'lo!.i

ll Rs.

A-4\B\B - ro napanenb,i{x nprM'rx ,4/, i PK. Or".e, AAt x ADr PK x PN,

in-

^,B'C,D,: . B.A|D , BAD g0'i- -A.B:C, ZABC g0'i . B,c!D2= . ACD = 90: ZA.D,C,- zADc 9O'.

2) nnou{uHa rpaHi.4,4,BrB J1eperr{rar rrapanenLEi nnorqrrsr!.4'8C i,4,BtCr ro na' ps,ler6Eux flpsMxx l-B \ A.8,. AA\ BBt rK 6tusi pe6pd npasn.,rrnoi npr.rsua, Toar ArAzB

A,B!

n&par€rorpaMt

AB.

AHanoriq'ro

B,c: IBc. B,c"=

BC, A.C"llAC,

A,c,= AC.

M,B,C,: MBC aa rpBoMa cropoHaMrr. ; i.|

3 piBHoc,ri rpxlilrrrnxiB Bnn,rfi Ba€ piBHicrb Bi.qnoBi!Hxx Kyri* Z,ABC = 1A,8,C,, IBCA = ZBICA2 i Z BAC :

n.iiii:.:

.i ; I ii: iil ':- ! t:Liiii:.: i

M,lt lM,N,. MN M,B = 2MB, N,B = 2NB, M N, 2MN.

3a reopeMoro @areca (o6epHeHoro)

263-

3,5

1,5

BM'

3,5

2,5

BN'

3,1

!i:;: TEOMETPI9 6yp.qa M.1., TapaceHKoBa H.

ZB,A,C,.

fpaAycEa Mipa fto)rcsoro s qr-rx EyriB 60", 60 : AArBrC, piEHocropoHgi.

266. 1)

MN'

776

cepeaEs niHis A,M,BNr:

Hexafi S.4JC

nipaMiaa, ocnoBa slioi

Ac : Bc, zc * r10', A,B,c, ll iBc

MBC : M-BC,

ciqHa rno

ntourrsa rpaHi ABS neperHHac Dapaiarbt'i niouru-

{BPt no napanenLHux npaMlr}. .4,8 i ArBr. i B, Bianosiano cepeavHn 6iqlirx pe' 6ep AS i aS, roMy 4,-8, - cepeAHs niHis .\ABS, tA o u, = ! *. AHanoni,rHo Arc, Ac. 4q = HLt

ABC

3a yMoBoro,4r

a. itli:..::lii:i;iii*i;:lliiJ:i

e,c, ic. e,c, =!"c.

iilliliit:;t:ti:ii:iliilliii rEoMErPle sypaa

;AC.

M. 1., rapaceHKoBa H.

t:l:l

777

AArBlCj

aa rp€rr,olo osHaKoto (rponopqiiHicrb cropft)' Ort4e, repepis -41B,Cr - piBHo6eApeHln rpElryrErrl(' - ^ABC A,q = B\cr tq: [0" zAt: zB,: (18O" - 11O"\ | 2: : 35' ((vrrr trpr ocl{oBi PiBI{i).

O6lpyHryBaHss AtrB. Ao 1).

nepepis AArBrCt - PilIIo6eAper*tii rpn&Yr]InKi

-8, = 180' 2 50':80'. AA,A,Cr piBHo6eapeE{n, ArBr: Bil-l' lAptq: lABC:30'.

75"

267, Ijexafr SABCD - nipaMiAa, ocHoBa nKoi pou6 ABCD' Toura A', A', C1 i rr cepeAltnu pe6ep AS, BS, CS, ])S BiAroBiAHo A,8,c, napa-'IFnbHa n,rourvgi A-8C finolrfiHa,4aS neperlrHat oaparlenbH

lroqrrsa

nnourxHn

cepealrlll, 6iqHIIx pe6ep OcKinErcI, roqrll'L41 i B, i BS BiAroBiAEo, ro.4,B1 cepeAs.s niEis AA-BS,

Blcl IBC i BPt=;BC, CD'

i L

AD.

3a yMoBoro nroDlr{Ha

,:,t/.t.i!:.:.] i1+:.i!1i:

BianoBiAHi

P-AS

272, ABCD{BPp.

ABCD

269-

aalla rpaneqin

'Jexaft Ocni"rrrn,4B I (t, ro a raxa. llro ,4-a I a.

rnoqrld

(,4,

BC)'

naparlenbsiii

rpsMa

3HT.,"1""3Jfl;:.'nroqrEioicHy€ae'*arrxva,

B -,,----\ ..2

-----\,

Br! II{o neperrrralorEcs' nnoqlrHx rpaneqii naparetbHi BiAroBiAso ABoM trpsMr-rM d i b nroulnH,r c. To.ai nno-'IHt{ A-BC i a napa"lenbri ra o3HaKorc rapanerbHocri tlnoIIlnt{. ToAi ABi npflMi,4-8 i

77S

!ti:

TEOMETPT9 EypAa M.1., TapaceHKoBa H.

IllyxaHnii repepi3.

rcy6 s pe6poM a.

ABi cri,'lbHi ro.rRn ,,l{

perrsy qrx nroqrH.

i N,

a or?r{e,

M i N BiAnoli4uo ccpea'rrg pe6ep 4B\ i Bp r qo npoxoa'rL qapo3 ro'tlcr M i N ra Ilesrp

MN -

M i N cepeAfilru pe6ep,4 MN cepeaHs niEis rpxityrHlEa,4jB MN -Il A,c,. OcriinB&r

UFHrp ux)r{Hboi ocHoB Hanen IlBaapara A,BCD.

AB I d' BD I d'

icHye Aesxa

nepepisy I

Ciqsa n,'lorlllsa Ma€ B nnoqfiHoro BepxHboi ocHoRu

6vrs napa'le'lblla n'os{ttHi o Ane rroultrsi G i roAi' KonI'I 6yrti raparenlsuMr{ Mo)riyrb aBi croposr raparlenorpaMa qIrM

ro rpnMifi,

no6yAyeMo repepi3 lly6a l]norq'tsoio,

napa"'lenorpaMa Monie

nnorqrHa napanerorpaMa reperuEa€ nnoqliEy c[

pe6pa

p\,zc.

xvrlr piBIIi'

/C -A qK npo-unexsi cropoErr poM6a' lB : lD = 180' ZA El{ npunerni Ao oairi€i : 18O" - 100" : 80"; 1J 1A: 1OO" lC : ZA - 1OO" tB : lD 2) lA: 4O", ZC - ZA : 4O", lB : ZD : 180' 40' - 140'; 3\ ZA: 60" ZC : /A: 60", ZB - 1D : 180' - 60' : 120".

268. He 3arni.{Ij. IlnourlrHa

rrorqrEi, ro i ?pern cro-

rapa,'lerblla rpaHi ZBC, roMy rIE nrolq}rHa nepellsaeTLcs s nnorl]asolo Zl-B uo trpsMiii PR, napa errr,l..iii pe6py zB, a s rnorqr{Horo ZAC no npnMiii PS, naparerLHin pe6

qor]rpl{1tyrElrlrl-r -4]9C, i ArBrC,rr floAi6ni, 3llaqrrs,

ro.ro&, orJr.ie, npFMa BC

- cepenrr'Ia pe6pa CZ ipar''jAtt ZABC. OcKrn6lrn nnoqulla trepepisy napanenbEa rpaHi .Z,4-8, ro qs nnoq*rHa repe"IrHa€rEcs 3 n,roqv rlolo ZBC ro rp€Mift MN, napa]lerL]lii, pe6py BZ, a s nnorqrso$ ZAC io pg:Mtii MP, apanenl,l]i pe6py Az. 2) Hexaii P ceDe,qrHa zA pai,inv- ZABC.

=:.CD j CPt

D,ll AD

i c, IIe Marorb cninEHr,rx 8(^ d.

271- 1\ ]fex it M

C,D,

o3Eaqae, ulo n,'1ontrrHrr.A3c He neperr.{Harorbca:

n,1oul/Ha o

MPN rnyllaErfi iepeDi3.

a,B. = \ AB. AHanori,rHo

{\---

BrcEoBo$: snrqo aBi cropolll-r rprkyasrrRa rapare,'r6Ei poEa rapanenbEa qiii nnoq'si.

ABC i A\B$t no raparrenEHrlx npsMfix '4-B i ArB,'

s&om2B ll s iAC o.

qepes ABi rpsMi AB i.4C, E{o repernnarorBcr, npo)(oAn?L €AlIIra trnorqrE.a ABC. fipa:ina BC Mae 3 aiero nnollxtsolo nBi .tri,rhsi ro.rK B i C, roMy 3a aKcio-

IIe

GAO'- 30') : 2 =

c[.

B nnoqrlri d icHye aesEa trpsMa a, napatetrma AC: AC I a. OcxinbKr AB c[, ro B rnor]sni (r icEy€ aeslra trpsMa 6, napajre"rrna;1-B: .4'B I D. Orlce, ABi trpsMi .4-B i ,4C, qo nepemsalorLcn, trrcn\v*v ABC trapanerbHi ABoM trpsMnM a'i b trrroqf]rr ct, roMy 3a o3lIaKoro naparen6Eocri nrolqurl,4,Bd ct.

ttr' t J'tLl

npx ocHoBi.

1A- tC:

rpnryrsrn,

nagrrii

- Bc qo I

MoTBBCeABC.

zc\:zc:5o'.

A= lC:50'

Hexaii-43O noBea€Mo,

Oclrinl,Kr AC I c[, ro

APt: BP, ToEr

27O. SaAaqa oropEa.

ocrdnb(' MN Apr j, Ac lApt, ro

npEMa ne-

BL i C,:

nenpl MNI

-ts

Cj,

/ \

^r:rii ac:a o:ua-

,{o lo naparpnLHo.ri nprMrrx. ': -l 3a reopeMoo npo naparefl,ri fl,rorqsllu ci'rEa n"ro- A rqrHa neperrHae sD*Erc ocEoBy rro lpsMin .4C, lla

panenbHrii MN. rtsa noo\oa 1s e-p", u.B1p HLrxHhoi o.HoBH. 3'eAHaBrrn cninBHi roqRtr,4 i 1l1 y ryaHi.4-4,.B,-B ra N i C y rpaHi BBIC]C IItx rpaHen i3 ci.{Horo rnorqnHoro, orpnMa€Mo nep€pi3.4-MNC. IIe piBEo6iqHa rpateqit,

a. il:ii:i:tili:il::::tili:i:.tiii!:ir

i:iil:iii:i:i:i:i:i:i:i:ii:i:i'.:.li:i rEOMErPlc Eypaa M. 1., TapaceH(oEa H. A.

i:iii

779

| ,4C aa no6yAoBoIo,

AM : CN (qe BlrnntBa€

CC1N sa ABoMa lrareraMlr: ,4Ar

3 IAA,M: Ax,t' = t'S

= ali

3 MCD: AC PA,,.,.

- 2AM

CCt

A1M't AM

: a' 4M = NC1=Z\

,rit -!-

(Eri aiarosanl $iaApa

rpsl{vrHljRiE '441M

3 piBEocri

=i*

s,,..Ka,, Kc

Jr' f "l

^ (

tF #

)t B.

,qlrHr ABox cl.'MirrHrx cropilrBB, i.4-B 6iq oi rpaHi'4-4141B ' IIo6yAyeMo nepepis rly6a rtorql{Holo, Lqo npoxoAlrrE .{epe3 ro.IHt ,K i P ra qeHrp rpasi,,!crc

P BiAroBiaso cepe-

!:,

t1r'i:.l!:'

:{i:::j::j

L t\'4,1.:.:4,,

;,:{i:n:+l l"3i.:.li!

.l.

b-o-C c o"xi'rruu KP

A-B'i DC,l A'B'' ,reii KBaApala ro l{P LrC' 3a o3HaEoIo napane"'r'Hocri trp€Mrx y rpo-

naparrenbaa t"opeto. npo napane'l6ni nroqrnr ci'Ilra nnoqrHa rlepe?{Ha€ rpoxoal'Irr' ae ,ri rpurrl el,-A,C i O-D1C,C no napanen6Erx npsM{x '(P i qepe3 qen{p ryaEi

'C|

,DiCrC

: AP' + AD" atE sx

PD =

Dct=

KP t*'=";' "iz

PDiR

7so

F,' o"6 rli t'"" = z

giaroHa& x3aapara 3i cropoFolo

3 LDcctt LABtBt

t:ii rEoMErPle

' en'=lg'=6{2

,Qc;

re ,E-T= E-=*

Jz 30 zJzo zo

9a'

q i d, trapanenbEi trnorqnHn, d i b nprvi. rtsi ix -Eepcrr.rHarorb BirnoBi,aflo B ro{Hax

lpoBeAeMo .rep$ rprMi d i D rnoulEEy. BoIIa reper!.IEae nrrorqrlln dr i cr2 tro rapanenbHrrx I]pnMnx A1B1 t A2Br. Ifo't1lp'jl<lrHHn A,8.8."4, - trapa4e,rorpaM, o.xinbKr. ) H-oro flporrInel*tni cropoHr raparenbHi. A B EapanenorpaMa nporn,re){(Hi cropolrr.r piBrri. Sira.rtrrb, /r4, : BrB,.

275. Tan, Moxcyrb. Hexaii d, i o, 1l!1116

y ,rcoAniii i3 qnx rnorqlIrr.

3u2a =al JtI

Eyp,qa M. 1., rapacetKoBa H.

l",L),ul

repanenr,:ii nroqqt{rl,,4

IIpoBeAeMo qepes roql!y.4 ABi rpnMi, nI{i reperrcra&rB nrlorqlrll1r c,, i c, y ro'rRax Xti X..nY i y, si.qnoBiaHo. flpoBeAeMo .repes trpsMi-4l(L i dyr nnoqnEy. BoHa neperEe nno' rqqsE crl i (I2 ro napare,lbntt x trpsMnx X,y, i Xryr. 3Bi,qffi isnnfiBa€ noai6HicrL rpuRyrHv HiB -4X jY r i AX,Y,. A 3 noai6Ho.ri rpxKvrflr}ris BrnirBac nponopqi.s:

AX. AY , AX, AX" AX, AY, AY, AY, .trxulo '4-Xr : .4Yt, ro-4X,:AY,iX!X,: - Y1Y,. UIo n rp€6a 6y,!o ,qoBecrr.

cr i B nepa-'1enEHi. Ha rnoDltrHi cr B3.snx roqxr,4 i B i npoBe,lr qeper ABi napa-renEHi npeMi. 'r,.rx nrii reperHynr [JlonrIIEy F BiAroBi.qEo B roqnax , i C.

3s sna'rrBic,rc ceoeaH6oi ,tiHii

"G 'fz t a'12 ai'r ' - 2PD KPt D., 2 "'--';=

Eexai

l,l)",

B$1: a, at=xn,=f,1

LDPA| PD!

FCi,

so' * sJz\ 2 l, 8.

'Cr

Tpaneqin DPtrC1 - flrvriasEii nepepi3 DP : KCb 60 !\DPA : ACrI(Br 3a ABoMa kereraMlr

IAD =

a'12

A1iA2r^4i8,.

f - cepea{Hlt lianosiaE )r pe6ep 3a vMo cep€aHs rirds I4-B,B: Pr l-4-81' BoIo, ro Pr (eH -p 6i,rHoi rpaHi DDra,a roqlJa flepF1r,tH) aiaroHg '!

Ai.iac:4o,

napanenbHi

OcKirE}ln P i

iti.:Q:;,;:1:.;.;

DnoqxHl,l a ip napanenbur. i npflva. oeperlrHsF trnoqxBy ct s roqEi A. IlpnnycrnMo, rqo qs trpsMa Ee trepeu,lEae n.rorqusy F, Bi3bMeMo B r,roqlrrli P ro.rEy B i rpoBeAeMo nnoqr{Hy 'y qepe3 rpsMy . i roq1ly B. II'loq]II{a 'y reperse rlnorquun ct i p no naparenbrisx npaMr.Ix d i , (r€opeMa llpo rlaparefi,Ili nno4ullr i ciqHy rnoElnHy). A"re sa trpsflynleElr.sM, I]psMa c EapanenLEa n,'Ioql,tsi 0, roMy npsMa . traparenbHa i oprMifi D (rK ,inii neperrH) rnorqss T i B). BlrxoAnrE, rqo B trroqrsi y qep€ ro.r&y A rposeAeiri ABi npFMi a i c, napa,renbHi npn\li; b. ruo cynepeurrr ar.ioMi napa,lenbHux. 3sa.rr.rrr,, trplrtryqeEHfi sel1pa3rL1r,se, i npsMa c fiepernEae firorqta Ey l].

274.

ciqHa n.'roqrHa nepeTlllrae 6iqsv rpaHb'4-4rBrB no nps-

Mii PK (a,{cioMa

-lo

q\'

273. Hi. Hcxaii

- alz sa a,Ea 3a MN Ac ^ sAV.i--_..lr^: ^,. -o'!2', i il, -q i"z=-ga's' r - +:,s,E\ s"" Bianosidb: d\15 Kv6, pe6po st(oro aopiBlrm€

B[cora rpane{ii,

t --- "J5

KP t DC,

MIf a ,4C

2\ He\an ABCDAtBppt -

=RF

utonoBtob: a\.15

- ""8 ^. 49.4! -'u'- , -'J' 3^AMKt AM!= MK: -AK i ux =,Eu= x" =rF:t

lpoBeAeMo

- ,Cr -

^ ^^ DC. - KP "" '224

alo

lbc-

n !a

A" = o'tr.'i'-' o'[z o't "\"

I(F

I ^ a"

M\. MN =rA.c,

flpoBenpMo

3a BnacrrBicrlo piBHo6iqEoi rpatreqii:

276. Hexai rnoqrEq a"E

iilillillii:ltililtii:::ti

[poReaeMo

rnoqrEy

;rit:ttiijtii{l{:ii:l:i

.repea

rapanerlni

trp.EMi -,LD

rEoMETPlg sypaa M.

i BC.

1,, rapaceHKoBa H.

lt:i

781

T* npnMlrx J43 i Bosa neper{e naparerLHi IrrorqnHu s i 0 no napa"'IenLHlrx 'C' napa-r1em'Hi' s'aqnrlr ;;;;, v q;"pr*vr'n'.a AEc' rpor''le*Hi cropo'L ABCD

277.

naPanenorpav.

A,B.

Hexafi napaterbHi trnoqr'IElt d

p neperrrHarorb croposu Iivra BAC BiaroBi'qHo

MN i rr',N . Toai AM,4lr' o AMr Mhx

'lf, g noAi6lrocri rp{r{vrrrlrlirB BtAM .4,\/ MN nnxBaF nponopaifl: Anr' erv, = ll ,V.' t2 , Y!. -" MN n,r = 1? !4 = ro r".nt , AM, M'N' .'la 18 54 BiAnosi)b: 1)

,p =?!:1! 18

72 1".y.

3a-

nDoBeapMo nnoqHHy '{epe3 npervli A,A ra B,B. V rpuxyru.xaxAtOB ra AOB IA OBt' - 1,4,cF2 a'< Beqlv:l"an]6:l,i' AtO - AO, 3a

241.

H6xafi

- A.4l,C,

:?ryri.Bt IOB\A1= ZOBA A"'le qi 1lvrr' - BHvr' piIIIIIi pisHocropoHsi nplr npsMlrx -4181 ra '4'B i ciqHi; B,B. ToMv,a.',B1 ll,a3. Airturlod.rBo aoBoalrMo, qo Bjc, ll Bc.

flapa"1erl'Iii' 3a osHa(om rapane,rblrocri rlJlorql'tl rnoqrHr,l -4,BrCr i '4-BC

1) A = 30". ,/8, . 60'. -c, 90': i\i:xr:;;i6; 2\ 1At - 50", /B\ : 60", tc1 : 7o". t,'tytt:..111ll irr,ii:.!i: nelt{LrB rosa ioro nnoqlrHolo' 27g. HexaiI ABC aaHr,tii rp - r{vrl1rK' ro'rlia ' p : :)',r::::::::l B\Apis]f:iB AD' BD i C' BiAroBiA ceperu-rsLr i N .lz, D - i PN cepeani niEii rptrr{vrsIjXiB -4C' MP ToAi { "o. siAroBiAHo.

nisii

MP I] AC, PN II BC.

ABi napanenbHi

B panenbHocri rnoqqrl nroqlrrlu ,4-BC i MNP

8,,

C".

782

!l:::

TapaceHKoEa H'

)

I]p.sMa

rrpsMa rrrecrr'rRyrHa nprj3Ma, B oc-

AAj

BBTCTC sa o3sal{olo

6i.rHi rpard npltsMs, B,C, (BnacrrBicrb aiarogani rpaB,.nr,Eoro uecrrr{yrI

Fr<

,4rr

A ,']e}I{srE

y rrorqrrHi -4.41r,, a 3na.Ilrrb,

MarE cniiEstrx roqoi{ 3 trroqlrlrolo BCC,. O't)t\e,

283.

i b' b i

rEoMErPlq svpAa M. l',

,re)i{rr} y nnou.{nHr c}, roqna

li t{a).

11'

c, f i c) Br-rsHa'Ia€ c&' €anEy nrrorqt{Ey, .tlla neperrsao lotrrystj cq, Cr,

Itoni{a rapa npnMti (a

ro.rna A

trpaBrr6Erj; uecrlr(yrHrti.

IlroquHa ,4,41rr, napanenbsa rpaEi

A,D, ..

nnoqrHn,

Z BiApi3Fa XY nenirrb y nnorqrFi 1,. Or)rie, cepeAuHr ecix BiApi3rii! e xiuqamu e napaie,lLstx trrorqr.rHax o i B neliarb y nnontr.rHi-f. EoBi sr{oi ner&rrB

' - n rapane"rrbnrli napaleJIbRi lpnvi' t'{i ne_ flnoll!.^Ht a, b i I perEHalor! nnorqltEy (x,, BiAnoBiAEo B roqnax '4,' s,, cq'

perrra rpr(yrsrrdB noAi6rii Aal{I{M.

M ua.pa"reftxo BY (nracrqeicrs rapanenbEfix nnorqrH i ci.rHoi llnorqxHn). Toai aa reopeMolo oa,'leca rprMa I neperrlla€ BiApi3oll AY B noro cepenxsi C. Tal{rM qDFoM, cepeArEa C uiApi3ka AY ,'re}}llrrl' y n,'lorqrl]i T. IlpoBiBrur nnoqtrEy qepe3.4-}. i roq&y y, asa,lori.rHo AoBeAeMo, rqo cepeAnHa

panenbHocri nnorqrH, 60 cr1,

xoAr.rrb qeper roqxy

282. ABCDEF4BIC,D,ErF|

ToMy 3a osHal(orc na-

280. 1) Hexaii

sa rperboro osllaKo$..

y nroqll]ri ll. qepe3 cepeAxHy .il4 BiAptuKa.4-B rpoBeAaMo n,'rorqqny y, napare"rrsy uorqsnan n i 0. Hexaii ].Y AoBirr,Hrri BiApiso(, r.iifrrri X i y.slioro nernarB y trnolr{rEax Lr i P BiArosiAHo. firoq sa, .al(a npoxoalrb qFpeJ nprvy BY , roq ,) ,4 (r a.iiAo, J aF. cioM), neperrrHa€ rnoIl{IIHy f no npnMii l, nKa npoB

3 pisHocri rp"qvrstrKiB BnnrnBar piBHicrb

3a BnacrllBicflo cePeAEBoi

nto neperzHa

AB.B,r,_o!,.

rloBroptrBirlr MipkyBaEss, AoBoA!.rMo, rqo

o1o o3nal{olo

i BC,

i c - rpsMi,

AzB' B'C' 4C'

IIe o3Haqae, rqo AA,B,C,

BO 3a yMoBoIo. Toai AA,OBT o AAoB

rlep

^porrncxRi

Axarod.rr{o AoBoArMo piBnicrb cropilr 8,,C, i,4,C,,. ToAi 3a rperboro o3Har{op rpn-

A\P _ 48 _BP=p.C. c,P 4C, .",,*, A2p A'8, - B, p - B,Cz C.p Aa( . "" ^ '

ct$ 2) 72 c]u.

278. Hexaii BiApisritl -4l' B,B i C,C Marorh crirlHv cepealrHv O' qo reperrHaIorscfl' 3a EacniAlroM 3 aKcioM crepeoMerpii 6vaL sxi aBi npsMi'

B1O

...A,,8,,.

firorqrsa,4.BC (Hac,'riAok 2 3 aKcioM crepeoMerpii) repersHae napanerEEi n,'lonrlrlr o i P no rapanen6nrx npn'

: 4.,8, :

R)1.uRA APtcr 4:4.C.. ....,4,8 C. piBHi. napa-1e,'r6rli mroqrsr. a, b Hexair c\, ct2, -., s, rorbcs B ro.rqi P. Ilnou{rHa, s&a npoxonrrB rrepe3 napy trpnM[x a i b, neperrrHa€ AaHi rnou]nHr ro napanenr,Hnx rpsMrx | 44 A,B, | ... I A,B ,. Alla,odqrro Brcr I B"c,I ... | 8,,c", 4ql1A,c;) ... I A"c,,. Toai A.41PB1 - A.4,PB, - ... - 4.4,P8,, ABTPC1 o A3,PC, o... - AB,PC., AA,PC, tu AA,PC, N... tu ^A,PC.. ern" rsac nponopuiii. 3 noqi6Hocri rp(Hy-HrKiB

Bro.riraxMiMlraNiN,.

,, =MN, -18 54

..., cr, no EapqnenbHrix npEM'lx. .4141 AzB,l4B3 | ... lA^B,,, 8,C,1 B"c" I ... 8,c,,, A,c 2l A.C1, ...1A,( ,. Toai A\BtBA.. A,B.BA.,- ... napanFnoi'paMx, ix cropoHr.r oiBHi:

Alt

KorriHa 3

nnoqrlr.4rB, i BrC,

He MolKe

AD,

BCC,.

Ma€ 3 r€BIIr-rMrI rpaH.rMr riy6a

crirblri ro.r

Kn, 3'eAEaBrrr'ix (aKcioMa a), orptrMa€Mo aBa nepepjljj: A.BD i BtqD\.

a' iiiatiiiiitii:lt::i!::':iii:

:i:i:::*i:ltiiiiliil::iii:|r rEOMErPlc Eypaa M. 1., TapaceH(oBa

H. A.

i!:l

783

IlpoleaeMo rnoqlrsy qepe3 6i'rt{i pe6pa.4-4t ra CC| Biapi3o( -4Cr re]IlnrL v Ain nnorqrEi (A € AA'C1 Ct e AAp'\. qeErpn lpoBeAeMo BiApiBEa,4rO i COr Ae O I O' jr AiarollarpaEeii ,4JC, i. 4B1Cp' rorrna repertrrlv netr. IIi BiApbns repertHalorb BiApisoit '4Cr v ro'rRax D

M i N.

qornpztiyrslrR

Apt :

O-4,O1C

or h rro ro r4-4

v LAPTM q

cepeasHaA,c,' o,N llA,M, roai 3a reocepe/jlr{ CtMt MN : CtN'

roql(s reperl,Isy AiaroHareii

-\. - :: ) "**

.tn] nt': 2) tm

nt')

I S-,,

n\d)

^,43C

- 4A,8,C,, k =:1:L =:

nr'roqrzrroro). Toai

-("#)"*" Biano*iab: D 4!-!L; z\ (-l)'

Ao' ll ocl.

ro.rlln neperllsy rnorql,Il -48,,r i B'C1

y LAM. ,. O - cepcArfla,aC. ON

A,'U,

loai

s-,!,.,

nps-

3s reo

nerron @a"reca M _ cepoAhFa l\'lci 14 N Vt^ i,oa rua, O - cep"rl,lHa,q .r \lO NCt, ro,i 3a reopcYorc oa'e'a M

sdc

k,.

ceoe

AB.h=4! l!)

A,B, =

3) Talce po3MinleHn.f, Mor{rnBe, sllqo r > zr.

ocEoB

Aiarosaieii piBEm( RBaApariB) i napanerbHi (60 ne)ftarb Ira niHisx neperltEy rapar€nlHI{x rpaE€ii Rv6a ciqllorc

flnoqy M,BC

"-,"

aHaxoalrMo aa ibopMynoro fepoEa.

24,5. Octd,rbris nyrr r- --.

c(m

-I:: BidnBidb:

xy6s. qornplrryrulrn .4O'C'O - napareaorpau' ocIlirbnrj aBi ioro c1opoEtrAO i o,Cr piBni (.'It tronoBrs]r

i rl

ll. *=94=Y OA

NIOqIIiIrI A]B'

'4'4!

ne}Iirr! v lrin nnoqtllii.

i Or

^,4.8.c.-

,\8,

Toai

cepeAsEa r4-lI: /rM : r14N' AEr-'Ioriqlio Iuo AM : MN: CrN' 10610' piBEocreii Br'IrnaBa€' 3 unx rBox i Blcrr Ainsr! BiApi3oe ACI sa rprr pitHi qacr"Ell' 2) ] :evafl AZD| i BDC1 - AaIIi IInoqlI] r' i CC,' flrolqxl{y qepes 6iqlri pe6pa

Hexan O

AABd

B AACN M:

IIpoBea€Mo Biapi3on AtC

2) Talle po3MiqeHs.s Mo,{nnBe rinbriu y Bfitraa(y, 3a AoBeAersM y no[epeAHboMy srna,ql(y

rC|

peMoro @aneca

.lm+ nl t m+ n\2 .s*.. I 2) | | m\.m)

BidnBidb: 1\ -:::,:::

flI.'\om>n,

napatenorpaM,

rR ronoBrIsr AiaroHa-nefi piBEnx 1(Ba.qpari;. A C i/4c rx niHii ncperrHv napanen6tsLx rpiHcii

,, 1n+n1' ^ JM4q=oMF.'h,=l-]"-"'

3 uiAroDiAEo

naparenbHsMu

oAHaRoBo Hanp{M"r€Hr-rMlr xyraMtr

piBHi, ro:

1) nyr Mix rpnMrMr ]{C I BC 60"j

284.

Po3rrsEeMo Mod(rsBi Bl'ttra.qRn $aeMHoro po3MiqenEn ro.rK]r O i napanenEHrx

n,'roq rldiB. 1) Ilnoquna, stia npoxoal'rb'rep$ trpflMi O'4 i 03' rep€rnHae nnoql-rHlj {r i p $o rapa"lerbEr:( rpnMl{x AB I A3,.

- AA,B,C'3 1coeoiqi€trroM OA. m+n

Toni AAoB

3Bi.qc BnDnuBa.. u\o

osEaKolo

nporopaiiiEi' i 3a rperLoro 3 $oeoiqi€nroM troAi6"i' AA'B1C1

-4,8C i,41.B,C,

MiC

784 !il: aEoMErPle

Evpga M. 1., rapacer,*o'a s. a'

L. 2

ii:!':*itr

iiiiiiiU iji:::::::!1S

iii,i:!iffi

ACB = 30":

B, i BjC, AopiBnroe ftyry

Milx BE

i BC

lnr-eac

zo.,

1aO" (IBEC +

3a rnacrsBicrro EyriB Mi}Ir rpnMrMn, qo neperEHarorr,cn, nlir{o ABi npsMi, nto rreperr{Halorb.r, BianoBiAHo napanenbHi aBoM iHuruM nprMr1M. ruo npperrHarorb .r. ro nyr Mi)rt treptllxMlr npflMxMr{ ropisHroc Kyry Mix{ apyruMIr. 3a HacniAr{oM is qiei reopeMlr Kyr Mix{ MnMo6ir{E}rMr npnMr{M[ uiA Brr6opy roqxr, qepe3 sl{y lpoxoAarb npsMi, raparenlEi AaHnM Mr.rMo6ixHrrM rpsMrrM.

AHanori.rHo Mornlra notra3art, tqo MOC N AAIOCr i LBOC - LB\OCr Toai BiaroBialii cT opoHlr rpli-

(yrHr'(iB

6) riyr Mir" npaMl.tMrl B, i C,r, AopiBHro€ rl}'ry Mi}K Bt i ' . ECD) = 180" (S0" ' 30) = 60".

AB k =-

Ni*$

5) rcyr Mirr{ trpnMrMx

xe *=J=-.

oA^.wn)

BrCr AopiBnroe kyry Mixi AC

2) nyr Mini rpnM,rMr.r ,4C i AlBj .aopirHo€ riyry Mi)n AC i AB - 60.: 3) Kyr Mixr npeMHMy .D i ,4,8, ,opiBHro. xyry Mi)n crrt i ]t,BL 90'; 4) riyr Mir{l np.sMr.rMr AC i Crr, AopiBHroe rc-\'ry Mixr -4C \ CD

roai6Hocri &'

iJlil{illiiilll:.:tiliiiiii

:':iiiiitlifiiiii:.!:j;ri:i rEoMErPle

Eypaa M.

1.,

rapaceHKoBa H. a.

tlii

785

286. 1) Hyr Mi,'i

rp.trM'IMn AC

i BlCr: ZACB

60"i

2e6.

2) ftyr Mi,{r rpnMlrMu AC t A,Bl tCAB = 6O": 3) lcyr Mi,i( rpsMtrM' CD i A\Bl ZADC - 90'i 4) Ryr Mi1( npnMrMn AC i

cp.

IACD

6) Hyr Mim trpsMItME Bt i C,r' i CD: 180' - (90" + 30") : 60".

49 1.

c,4= cD= 4

LB.ABTABAB4 cD, cD I

rtD\ CD I

AiC,rol

1) trpoellqi.r rocRn C He Motte nettarr Mirrc rpo€ErlisMr ro'roll A i B; 2) npoe&qi.s ro.rlin, Ee Mo]*e ne*raru Minc npoelrqisMs rorroH B i C; 3) rlpoelrqiE ro.rRr B rexcnrb Mir{ ro'rKaMn A i C.

3o";

qe ]rvr MbIc trpnMl,lMlr BE

297. fiprr napaierEnoMy npoeriryBarHi s6epiraerbc€ Han€BEicr6 roqoR npFMin ra tropaAorc ix po3MiqesE.r na rp.sMin. ToMy, nllqo roqKa B netnrrE Mil*l roir&aMlr

=:zAcB = so't

5) ftyr Mbrt rpsMnML BE i B,Ctt zcBE = t/ABc =

294- Ha Mar.772 He 36epernncn

S6epe.nrcn S 8, napatenbHe nPoefiYBaHHe

AlBpt

l. naDanerhHolo .rpoeKqi.Io ro'rEr ' roqKa. nprvoi - nptMa' roqoK npoexrvBaHHi s6epiracrbcq HanF)+t'1i'rb t. rl;; ix posMiqeEHs Ea rp€Mii. uopsAori"np,""""";"y

npeYiii ra

3. Ilpoeriqii napanenr,Hlrx np.sMtx napate,l6lri a6o 36iralorl'cn' EKrqo BoI{r nex(ars v nroullrHi, napane. 6sifi Har ptM) npocKrlBaHFt' l. npi nup-.rono"y npoeFrvBaHHq 36epira'rbcF piBHjcr6 ra nponopriiiiHi'rb .BiApist{iB, rqo reniar6 sa oAriiii rpsMifi a6o sa naparenr'Hq)' rpnMlrx' Bai sol npr $aparenr,EoMv npoeErvBaEHi fe s6epiralorrcs: 1) AoBLnsa BiApi3(a;

2) Mipa rcyra; pitHicrb LYriB; 3) repneEAr(ynspEicrb nPnMI{x;

4) piBEicrb a6o nporopqifiHicrr' BiApisltiB'

tlti

@irypa, sKy npoeIi169

IpsMa

tr,

IIapanenr,Ha

-4rBrcr

CM -

p'rqa

IpnMs MtNr

lpsMa ,\4N

"''.' I

170

lil*:;:.i:.!:.:

AA1, BBb CC,, DD,

171

,:11./l.,.1:!':.:.i

A\B$PI

irrl:.1{.li}:

npr rapa,lenlHoMv rpoeirvBalrEi 36epiraer6cfl l{are}Ilsicrb Oirvptr cgoe My (nacy Oiryp. Torn rptrnyrHl,E npoerirverbcn B rplrivrllrItr' JI lne v BuraARy' lionr nnorqsEa rptxvrlrlr&a trapane,'lr,Ha l]arlpsMv rlpoeKryBaHrla' Brrr rpoe(rv€r6

292. Hi,

293. IIi, npoe(qierc ilorrplrltyrHl'tRa Monie 6yrn qorI{plrlivrnlrK a6o BiApiso( h' rraaRy, fl Irqo rnoqr-rHa rpn}{vffir(a rapan€'!6Ha sarpsMv rpoeKrvBaHlrfl )'

294. t)3 . 4;

A,B. AB 2 ,-=;;

295. 1);:!=

286

3)4:9. 2\7.It - AB, AB 2 ^.48, tt

ei,,"

AB 3

Ec r ' "' e?, a7

li::: rEoMETPlq sypaa M' 1., Tapacexroea H.

r.s

NreAia'la

,1erBIi1Ix Bi,qpisft iB He s6epiraerbcs). 3a yMoBoo,4-M MeAiaIIa, npoBeAeHa Ao 6iqlloi cropoHn BC, roMyMr cep€Arrna B,C,, 60 s6epi-

l,l\

ra€rbcs n]}oropqiiiEicrE BiApisxiB, qo nexiarl' ro6palKFHHe Ha oaHin npavifi. Orxe. ArM, .

/, I \"

rpr.rRyrEqny ne o6oB'.ssrioB-9 3o6paxiy€rbcs BEcororo. An€ B EarroMy BI{tra'AKy Brcora B, trpoBeaena ro ocuoBl,t piBso6eapenoro rprrriyrsnxa, roMy BoHa oaHorracHo e MeAiaxom i 6icexrpucoro Hyra trpr Bep rEi B.

rlorrapl{t yrElrx

ABCD

:g0'i BC:4,AC:3

CM LAB, IACB

rprxyrlInK;

-M1B'C,

AA1, BB\, CCI

AABA

He s6eper,1rc.s

lepnssAuliy,'rspHicrb rrpsMnx se 36epira€r6c-f, ,4 rpr napa-lerLHoMy npoeKryBaHHi, roMy Brcora

Kll

a' 'il:ii:ili:i:.:'':!:i:atl:jlt!:;:iii

pilHocropoEnin; Bircorr-r i 6iceRrpror

299. Ha opsriEani B'scyeMo BracrsBocri (biry?I,. ByAy€Mo AoBirbnri AATBjCL (piBnicrb Henapa

Ntenr.aljtl AM

KK1' LLl

BK, CM,

S6eperJllrc.s

ne,Ilarb Ea npsMrrx' nlo neperr-

npoeEryBan6-

cepeArrEn cropiH

Ha Man. 1?3

, 291-

LABC AL

rprr{yrHxE;

M, L j. K

OcEoBEi BnacatrBocri

"S,7 \1,

Or)"e, so6pax{eEHsM Br.rcorn ao ocEoBr i 6ic€r(rpnct Kyra trpr{ Bepffffri BD pa BrD_ rprkyrHxHa A B{t. LA]B{t rx}KaHa Epoexuie.

300. [o6yAyeMo opuriEan rpr.rriyrEr(a i 3'rcy€Mo

sa HIrM BnacrrrBocri

€ Meaia-

uyliaEoi npo-

e$qii. npoeK4i.ro l

pr.rkv rrrrrRa L rpxxyrH,ax. norHaqnMo iior o -4,BrCr. 3a yMoBoro lC = 9O". A]ne nprj napanenbHoMy npoe(ryBaHHi nepneHArlcyrf,p icr6 npsMrx He 36epiraerscs. rouy AA BrCr He nptMoRyrs i:i. 3a yMoBoro M, N i D .epeauBr B'aEoBirHo cropiR AC. BC i A-4. O.xi,rbKH piBHi.lb BrapiokiB. oro rlelHarb IIa oaHift npnMiir, s6€piraerbcs, ro Mr, N1 i 11 cepe' Ar.rHr cropiE 41C,, BPt i 41Bl BianoBiaHo. Toai A,Ir',, B MI C,, 3o6pax(csHs Mp4iaH lp}rHlrnpoeKuiifiorocepcAHi\ HxRa. MA - N Dr M D

i!li:ililinalliil::::::

rEoMETPlg EypAa M.

1., TapaceHKoEa H.

a.:l::i

7a7

3O1,4.4'8C

- trpsMonyrrltri, lC:9O", M -

cepeArrra AC,

cepeArrrla CB'

KM L AC, KN LCB.

BiApirxiB. 36epira.r6cs raft o*( IIopf, lloK por^4iueHHfl roqoK Ha npsMirl. ToMy cepenrHrr M i N 6iqssy pe6ep opxriHany npo€RrytorLca B cepeAssn Mr i Nr rpaneqii.{1BrC!rr. MrN, npoeRqis cepeAaboi niHii. 2) i 3) po3B'r3vrrbcr aHanoriqHo, MiHsrorEcrr MicurMx nxlue 6yHsr{ Ha Man.

npoeK(i.ro rprkyrHrlKa c rpr'{KvrHtrR. fiffiHa.IlrMo iioro,4'8,C,, npr{ napa-renhHovy npoeKryBaHsj oepDeHArtcy ^, nrpHicrb nptMux He 36FpiraerEct loMy AA'B Ct "' IIe e trpsMoKy|r:{IrM.

3s yMoBoro

ML - cepealrlrEni? repreEAsl(ynsp K : IACB : 90' , I\i &v'tl,r -

Eo r<are'.a AC. ZAM

BiAroBiAEi orlr{e, MIf

rlpr trpsMl'x MK i CB i ci'rHin -4C' tr l] BC. ToAi 3a reopeMolo @aneca

307, 1) 106

c€peAnEe -4-8.

Ananori.rEo trN AC, CMKN - Ilpttuot v'r:d.d:R, OcKj-nbK npr napane,lLHoM! npoexrvBairsi 36epi-

racrEca piBHicr! BiapisKiB oasiFi nprMoi. ro cepeAlrl{lI cropiH Ar43C, suasurt' M, sRrqo M, N, tr

ArB1. - cepeArna npoBeAeMo BiApisRtr MlKi ra N1Kr.

peAnfla BrC1,

AA,B,C,

.K1

EBa'q

(Ba'qpar 3O3. Asarori.rHo ao Ni 302 rapanerEHolo npoeliqi€m &Ba'qpara Monie 6yrr i por6. a,re Hc voxe 6yrx rpaneqit.

He 36epirae1Ecs, a

l;,*;:.:ta,t!i

/,;l:llti:i:

qorrrplrKyrlrllK i3 trapanerlBlrIrMn croponsMq raparenorpaM -4,-B1C1Dl. M, N, P, K - cepeI.sau cropiE npnMorilrnt{K4.4-8c,. OcF(inbli, 36epiracrsca Hane)lrHi.rb rorroR np'lMii ra ix nopeAoK, a ral{o}t{ piBgicrb BiApi3xiB' tqo,rex(arh I{a oAlrii rpsMifi, ro rpoeRllii M, Nr P' Kt Aa' lrrrx ror{ox € cepeannaMr.t cropiH ArBl, Bpt, c\Db -4tD, rpoeRllii AlBlCrDt Orrae, MNp N,P| PrI(,' M,K, Biaoi3}rx. Lqo cnonr{alor}' cepetr En cvMixBiApi3oR, rqo 3'€A1{v€ Ht x cropil{, MPr i N$1 cepear.rElr flporlIne)*cEtlx cropirr.

305. Ocrcinrxt npr napa-renr,EoMy &iB rapa,lenEEux

e(qiero rpafle{ii He

Dpoe&ryBaEEi s6epira€r6cs rponopqiiiHicrl' BiApis'

1., rapaceHKoBa H.

napanFnbHoMy npoeHryBaHHi 36epiracrAcr

ha- a

ne}t(sicrb ro.rolr npsMr.rM. ix noprtor porMiu{eHBn i oponopuifiHi.rb BiApirRiB orHi€i oprMoi. Toyy Binpiror KP. ulo 3'cAHlc cepe4uHn AiaroHaneii rpaneqii -4BCr, flpoeKryerlcs y BiApisor -K,Pr, r1o B'eAEy€ cepeA$Hn AiaroEanen rpaDeqii

,{rBrcrrl.

3) po3B rryrorb.e aHaroriqHo. MiHaor6cn Mrc6yrcBr.r

Ma-r.

BaAa.ia onoplra.

qe x3aApar. 2) npaBr-rnlHr.rfi qorr-rprr&yrlrsx &Ba,4pare nporrnexHi croponu piBEi i naparer6-

Hi. npI-r napa-renBHoMy npoeEryBsrjl1i 36epiracrbcfl napanenbHicr6

nprvrx

1a piBHiclb BiapirKjB napa

rejlEEqt rlpfiMnx, ToMy npoeftqierc npaBnnLqoro qorrpnriyrHrrria (EBaApara) e qor$p$nyrHrn, y sfloro npo,rlrner{Hi cropoHM piBHi : napa-^er6Hi. 3Ha.rnrb, npoeEqi€ro KBanpara € naparenorpaM.

Ilenrp (BaApara roqfta neperrHy ioro Aiarosareii. OcHinERn rsa€Mse posMiqeHss roqox Ha flpsMijt 36epire€rbcn, pa roqna O reperrrHy Aiarosa-nei sapanenorpaMa trpoeEqii.

ro DpoexqiF qetrr-

raer6cs,roMyArBlCrDl rpareqisIlepiBlro6iqHa.

rEoMErPlt Fypaa M.

flpr

He 36ep:nicrb.s, roMy Dpoelruir pi8Hocroponsiii rpIIIiyrHuR. qe roqfta neIleErp pilHocropolrEr,oro rprzr{yrHllfia pcl d) rioro MeAiaH. Bxcor i 6icpkrphc.neprenAr.rnyrEpEicr6 npsMnx i rpaAycna Mipa nyra He s6epira€rbcn, ane 36epiraerr,c.fl B3a€MHe po3MirqenHs roqox sa npnMifi ra piBHicrb BiApisriiB o,q*iei npsMoi. ToMy .l4 i N cepeAr{H cropin /.C i,43 BiAnoriAHo, BM - so6palrcesEs i C-l[ - trpoeftqii Me,qias, a rorrrla ix repernHi O rpoeftqifl qeHrpa Aar{oro Tprr(yfnlrRa,

306. -48c, - rpaneqis-oplIlitran: AB I Dc, AD = Bc Ocrdrbrsr rpr naparenr,soMv npoeErvBaErd s6epira€rr'cs Esnet{Hicrb Oirwli cBo€Mv qornprrR}"I H'rn '4,BrC1'r' R,,lacy Oiryp, ro rrorr.p cyrErr(.4-BC, rpoeRtyer!'c€ B lapsrenbHicrE trpsMl'Ix ra rporopqiisicr6 BiApisKiB napare''lEElrx s6epiraer6cs' roMy rpoeKqis ?4.181c1rr e rpafleqiem. PiBEicrr, Henapanenb1rlrx rpsMl{! Iie 36epi_ lla{

npoenIli€rc

ri,'IERrr aoBi-11,8a rpef, eqijr.

788

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AoBxpHs B:api3Ka

talloxi s6epiraerbcrl Hatex{liicrl' xnacy Oirr'T, ro npoMoxie 6ynt rpl,Illvrlxrc i poM6 (ocHoBa HepiBIIi)' a MorRe 6vrrt

rpsMrx,

Bnac,rlrBocri, aKi

1) npr rapanerbHoMy npoer-iryBaHni B6epir6err,cs HsneFHicrb Oirypr cloeMy nracy ibiryp, roMy rprrriyrl{nl{ npoeftTy€rEcd B Tpr(yTnn&.

qor&pr ryrsr{R.

308.

napanenr'- '

nicrb 36epiraerlcs, ro rlpoeRqi€rc npsMoRvrI IKa

:i : ilrl:i:::::!i:i

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' q.sME ''IrIIIe

3O4. ABC D optrriHarl npsMoxvrstina. OcllirEllrrpEEapanenLEoMynpoeftryBalr reprleH_

".1, ---...,,

rpareqii /3C, € AoBi,qr,na rpareqi.n -4rB,C,DL. fnrqo AB 6ir6ura ocEoBa,4-BCD, ro.41B, 6ir6-

302. Oc&inl'rcr npr napanenLEoMv npoerirvBaEEi 36epira€Gcn rapanenEEicrb i

i:#*iinlii

napanenbAoMy opoexryBaHHi. a6epirarorrca.

rrla ocHoBa npoeKqii.

36epira€rbcn rpa.qycEa Mipa KvriB, ro npoePrqierc raparenorpai{a Mor&e 6yrri par i pov6. ane Fp vo,Xe 6yrx rpaneqis.

P@r.rsneMo oprriHan rpaneqii.4BC, (-43llCD), 3 lcyBarn BnacrrBo.ri, rHi 36epirarorbcfl npH

S6epira. rbcr napa,re,I!Hic1

cepeariEaA,Cr, N1

Eyltanatrpoelcrlis.

ar{Eynspsicrb npsMLIx

fl&nlo BiApi3Rs ne)r{arr, Ira oAniii trpsMi*, ro BiAHoeHIIs lx fipoel{qiii AopiBHroe BiAHouresEro caMfix

a. li-:!:ii:lliltiiil:.:::;i::l:

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1., rapaceHKoaa H.

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"ffi"

rrrecrr ryrEr.rF(a. rA,BCO i ODEF - piBlri poM6n s BiAloBiAno flaparen]'IIljMx cropoHaMl{ Ilpoe&qierc polr'.6^ A,BCO € AoBinbHL* napane''lorpaM

A,BrC101. Oc$inbrcn rptr trapanenr'IroMy rlpoe&ryBaEIIi B6;piraerbcs napa"rreJlbllicrb rpsMux i piBEicrb BiApis(iB oAEi€i rpsMoi ra napa.renbEnx rpsM,ix' ro peury

Bep rH rpoe(qii InecrljKyrlrrr(a 3EaiiAeMo' ro6vAl'BaB : ArOr Err.r Ha rrpoaoBlr{eEEi cropolln/.ro1 EiapisoIi opt cpt olt: 4BQ1D1EI1 r{a flpoAoBdreHEi clor -

IlpaBrna 3o6par$eEEs nptr3M$ 1. lIIo6 ro6yayBaru 3o6panresirs nprgNttr, ,qocrarHbo no6yAvBarrr Mlrorol{yrHu('

€ 3o6par{ieEnsM ocEoBI'I flp{3Mtr (a[B N, 308)' 2. fioriM B Bep zII MlroroKvrEl{ria rpoB€crs lapa'enLHi npnMi i Bi'qrcracrr Ha nrlx pigHi nispirxE. OcRi,'rr'ftfl B rpaB{nElriii trptBMi 6i'tHi pe6pa nepreHA}rl{v-

ocEoBIr,

312, Hexai! AB

Biapi3oK ae'ftoi trpsMoi d. BtubMeMo Ha Hr,oMy roq(y C i npoBeA€Mo rrep$ roqt E A, B i C napanenbHi, rpoel(ryloqr npsMi.4?4,,

aaj i ac,. Ili npeMi ncxarb B o,qeiii rrroqlrHi. sHa reperuEae tr,'Iorqrny c[ ro rrpfMii or. To.{&r,{r, Br i Cr npoeftqii rorrorc "4, B i C Ea rnoEtlrHy c{, roqKa Cr nel*rt6 Mi}rt roqftaMl Al i .B1.

y- = +t.3o*pcMa. 'eso BC B,C, C cepeArrra A-8, 'ro Cj cepeA{Ea,4rB,. ulo6 troAinurn linpi3oK -4-B y liaEouelrHi 4, norpi6no: oa,leca: Ba reopeMop '

rrvKasa tpoe(qis

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rDoeRqielo BiApi3rca a6o rpoe(qiero MHoror.yrHlrKa y Blrtrsany, .altqo rnorqrrHa MEoroKy?Er{Ka napanenBHa HanpsMy npoeKryBalrHn.

311. BiApisoK MolKe 6yrr

ro ir( Ann sao.IHocri 3o6pa*{alorb Beprr'rKanElrrMr

3. ItiHrri Biapia&iB 3'earrarlr rlocrriAoBEo.

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BA AB,BD BD TaHxMqxnoM. BiaEor csEr ftBaapariB ftareriB ropiBHmc

310.

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npoBenel{a Ao ocroBtt, DE - froro Bltcora, nepnenar4xynap, npoBeAeH fi .4o 6i.iHoi crooor'rn. OcRi,rLxx npx napanerbHoMy npoekryBaHHi He 36Ppiracfl'cs piBEicrb Biapisnb, EHi repertHalorEcs, i Miplr &yriB, ro npoeKqierc rplrRyrHgxa AiC e AoBin6HHii rpllliyrsnR.ArB,C,. BI,cora BD, sxa e Meaiasorc, rpoel{ryer6cE B MeaiaHy Brr!, a rpoBiApiso& ,tll, Airl'Ir! croeRqis repteHArriynspa ,Il

BH 4.24' 2304 - 8,c, 14' 196

3 Bepulrss C, rpoBeAeEoro Ao Aiarolrani e BiApioox C,.E,,

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315. Ipoexqi€to

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a. it:;:ttluiii:lili:ti{lil:i

AeHoi 3 Bep !.rHr.r rynoro r{yra, e BiApisoH BF, Ae Brcorr, npoF - cepea ll AD. CH - 3o6p&rceEHs BeAeHoi B Beprlllrill rocrporb riyra C, ,IJ : ,-F. flepeph npr3Mn,.rxt{; rpoxoarrr' qepe3 Bncory BF, Ma€ s pe6poM BBr cni.'ILlry ro'{y B i rpoxo.arrE -repe3 pe6po BB,, 60 ci.rHa rnoqulra sa yMoBoIo napailenlEa 6iqEoMy pe6py. Bol{a reperrrae ocsoBLI ro rpsMllx B.P.l BF. BB,F,F - utt'KaElri:i nep€pis. Ilnoqusa, .rl{a rpoxoAsrb qepe3 Brcory CH, npoxo,qxrL .repes pe6po CC,.

324. LABC - 3o6pa8eEris piBHo6eApeHoro rpqnyrslrka. 3a yvoBobA-B AC b, BC : a. Ha 3o6paxeHHi piBHic'rL cropiE.{C i.4,8 ra lenlr.r'rHn (yriB H€ s6epiramrl'cn. UeErp O lco,ra, Brr.IcaHoro B ocEoay, qe rorrEa teperrrHy 6iceerpx. rpflKyrHuKa. y prBtso6.rpcHoMy rpxK).THxKt 6ice{rp{.a Kyra npv Bep!xri € onHoqacHo froro MeAiaHoro i Bscorolo, [poBeAeHolo Ao ocEoBr'I. Ocrdnbriv npr, ro6paJr.eHEi 36epiraerbcs piBHicrE BiAptu A RiB oAHi€i trpnMoi i He 36epiraer6cs treptreHAl{IlynnpHicrB, ro MeAiaEa, , e so6paJrteHllsM 6icellrpltcr nyra A j. Brcoar\, npoBeAeHo-i ao ocIroBI{. O e AD, OD : r paaivc Bfincalloro Eona.

iiiiti:lti:tit:;r:ilJlillil rEoMErPle

/"h\

EypAa M. 1., rapaceHKdEa H. A.

ii:::

795

f flo,roxenirg ro'rxt O sz3Ha'ra€rLcs liAIIoureH:,dAlI Ao I OD. SEaiaeMo

ioro.

Oc$irLHu

oicekrpuca Kyra C.'to AO tOD A

\t AOiOD=8i:

AC tCD

t;BC

at3: 2)AO: OD 13:5.

flnorquHa, slla fpoxoatrtb .rep$ To.rftt S, C i O, trepergi]a€ ocEoBy no [p'IMii CO' nlo neperlrsa€ pe6po,4-B E roqqi f, S-K - niEis treperEHv ciqsol trnotqtrrrn 3 rpal]Flo,4-BS.

ASCI(

yxaEltfi nepeptu.

flpa3tlna to6yAoBs 3o6pa]i{eHEa pitHo6iqHoi rpa_ ii El-rcora posusEyro ! saAa'ri Nb 321. 3o6pexeHlrsM ,DaHoi rpsneqii c aoBinLHa rpaneuit -43CD, 3o6p${e:rHsM ii Bl'rcorrr - BiApi3oR DH' FRrifi Airxr6 ocsoBy.4.8 y Bi4HouleHl{i:

325.

Ilexait ABC

n€qii ra

AH : HB.

23-)2,24 *J2 6, =

223 2t'22 aH I EB =!!:3 .lt!

SrIt - fiIyfiaEqii nepepi. 326. Eice{rp{ca riyra B AirItrL

Aparr.

napanenbroMy trpoeRryBaEHi 36epirarorEc"E rapanenbqicrb npsMl'x, piBEic,rE Ha napanerr,Hnx rpnMnx, ra ix rponopqiinicrE, HanernHicrb i EJacvBe po3MiueHHfl roqor Ha nprMifi. ToMy B rpoe&qii AaHoi Oirypn AA,B,CI ne nprvoxyranir, a npoeKqisMr RsaApariB e napanenorpaMrr, npsrroMy BiApiBKrj ALCj i CrD, ra FrCr i C,B, :rexaru na oguin npaMin, .K,F, ll,rp1) B,Et, KA) F$tt. DF\.

.1-,

rr.

trportuer(Hy cropo_

36epirac

rb.s napa-

nerbHicr6 nprMfix i nponopuintsicr6 BrjpirHiB. Ilto nFxcarE IJa oAHifi trp.sMiii a6o Ha napanenbnr-rx $pnMrrx: Ats II DC. AB = DC, AE = BF, Touy A;rs no6yAonu npoe(qii 6yAyeMo raparenorpaM .4rB1C1Dr i na npoAoBlrieEni cropoEn-4rBr BiAKnaIa€Mo piBHi BiApisK'l ArEr i BrF1.

EP\Cpt

t\ADtDC=2t3i 2lADtDC-514. 327. Pos.,lsl{eMo oprriHa-! - AABC, y tKoro -C = 90". BC = a, AC : b' Ileurp O onrcaxoro Haaftorro sboro fiola rexnrs y cepe*rni riirorenysg. UeHrp Q BrHcaHoro Ho,ra roqxa nepervHy 4

331

6iceRrpxc 8J( i CD RyriB 3 i C. 3a lracruBicrro 6iceftrpuc,{ nyrs AK i Kc - AB I BC = . I b. AD : DB - AC i BC = b I a. 3 po3r',rsHyrHx Bnac rBo.reii npx

O, D, N 4---'128' l\ -\ l\ )6. t I \ )<\/ -W^ ^' napanenr,- I \o HoMy npoeftryBaHHi r6eprrarorbct raRi: I \ D a) Hanexflicrb i sopflaon posMitrr€HHn ro'IoR /( l,/\

I >-- \

6) piBHicrb re flponopuifiHicrL Bi,rpisHiB o4Lr'q -\ !:i€i npsMoi. B C Orxe. npoeKui.rc T p xyrHxxa ABC F AoBinL_ Hui rpuftyrrllrx ArBrCr. OL - cepeA{Ea cropoHs,L18, - npoe(qis qesrpy O osl'caHoro fioIa. Ill,06 sHanrn rpoelcqio Q qeErpa Brllrcasoro Kona' no6yAyeMo BiApisoR B1trr ra(' ulo6 AL-K1 : trrcr = c : b, i CPv t\o6 A'Dt I D\811),{1r, I rldr : 5 : 4; APt : D$1 = 4 i 3i 2) A$t I KPt = 17 | 75i {Dt : D,B, - 15 : 8. r:Jil

330. B opllrisan6sii Ao6yAoBaEifi rpareqii trCF : BF, A-BCD - $Ba4par, AE I]px napaie,lbHoMy opoe(ryBaHBi

TaKrM 'rr.rHoM, flpoe&qi€lo AaEoro rptnyrHtlKa e AoBirBHai A.4BC, Dpoexqielo 6icerirprcE ftvra Br, nlrtri Ain]Irt' cropolly-Ac y BiAHoB - BiApi3o( ureEEi,4, i DC: AB I BC: n: ,' (nqB. Nq 313).

7e6

rcBa_

aiApis(i!, qo r€)Itar6

Hi cyciaHiM cropoHaM.

np'rMii:

Ha cropoHax nlroro no6yAoBsHi

flpr

ny AC rpa*yrsHxa AJa Ha qacrvHl-r, nponopuift_

- rpsMoRyrnrii rpr&yrHi-rl{,

rEoMEipre 6ypaa M. t., rapaceHKoBa

a. llil:ililli{lll:.ii::.:i:i!:i:

srl,.IlaEa npoeftqis. -Er

Po3fnslleMo Oirypy-oprriqan. - npaBnn6Hni, iioro Ao6yAyBanq Ao fipnMoEyrEoi rpaneqii: qepe3 BepusHy A npoBenrr np.sMy, rapaner6Ey BC, ro6y,qyBanu C, - flepneHAniy,rsp Ao qi€i DpsMoi Bucory

A/tsC

rpatreqii, aRa AopiBslo€ Brcori rplInyrElrrca.

focrpxfi Kyr F ra yMoBoro aopiBHrcc 30". ICBA : IBAF : 60" trl{ BHyrpilrHi DisnocropoEHi, roAi

l,4BI - 1800

(60" +

30o):90.,

rooro 4,46f - EprMoHwHnfi, i A-B = : AF 2 riarer, nlo nelRnrb rporlr Ryra 30..

To6to AF = 2AB (noABo€Ha cropor{a

rprrriyr

Hnxa).

LACD ICAD : 60., ."]oai ZACD = 30" i AD = ! AC. 3 ycix posr,rnryrrx BnacrrrBocrei qri"yp op" ,rulpurr",rrrroMy Dpoe&ryBarni 36epi

ra€rr,cs rapa"renbqicrb i rporopqiriHicrL BiApisdB oAEiei a6o Dapa-lerrbErrx npsMrrx.

Ans ro6yAoBn npoeftqii KpecnnMo napanenorpaM ,1C181E,, roasaqaeMo cepeAssy A1 BiApisfta DrEr. AArBtCr rpoexqis AaEorc AABC. Ha rpoMeHi, 1,gr Bi{K,ra/ra€Mo BiApi30l{ AtF. 2ctB,. D.C.B F, ulyKaHa rpaneqifl.

j::tlt::ilii{.tllt:iiltii:it rEoMErPte Eypaa M. t., rapaceHKoBa H.A.

:l{

zsz

332.

PosB'.a3aEHs y

333. 1) Ocxiftrcr

niApyqs

4) no6yAyBarE Aorx.{Hy B roqqi ,', napa"reftny ,41C1r 5) EpoBecru trpsMi A,O| B1Ot, Cp1 npoeRqii MeaiaE M1B,C,j 6) npoBecrr Aorr.{Hy Ao xona M1?1 i N'nr; AMrPrNl yRalrrrtonrcaH'n.

tY.

opldHani Bep lllr1, FBaApara nel{arb

ncpnpsrt{xvntpHvx arauerpiB ro A.rs no6yaoB[ rpoenqii (Baapara' BrtcaEoro v lcorlo' 6yAyeMo eninc rpoeftqirc xona i npoeEqii ABox B3aeM

y xiHuex Asox

B3acMHo

Ho nepfleEAnriynspElrx AiaMerpiB (A!r8.

BtrIICAEOIO B I{ONO.

332). aiaMFrpiB' npoeHqill) kBarpara.

cropost

nnxcanoro npaBxnbHoro urFcrrtsy HuKa .niBna4arcrb.

rriiiHicrb a6o pitsIricrb BiApi3riiB oaEi€i a6o naparlenbl{ux rp.nMlrx.

u!,lY

2) B opflriEaj1i

BnucaHoro

IIptr raparcrTbEoMy rpoeliryBaEEi 36epira€rr'cfl rapanenbHicG npFMux ra nponop

3.aHasurx BiApirka-Mr nocri40BHo KiHIli onep)Hxvo napdneiorpaM A-BcD

335. llesrpu

rcBaapaaa, ontrcaHoro EaBRono

riorra, e AorrqHrrMn ao Rona B kiHqfix ABox B3a€Mlo nepnefl

Anliynspt{rx AiaMerpiB

Ori*ie, npoeEqi€to I{Baapara, onncalroro lraBl(ono r.ora' € napan€,lorpaM.4-BCr, flft{ii oAeps(lrMo' ERUIo npoBeAeMo Aors.rHi Ao l{ona B rdHII.sx npoel{qifi ABox B3a€M Ho nepnesAllliynsplrlrx AiaMerpiB y roq"ax Il' P,

Bis.

O.{i,1bKr pH

llrn ll'lD i '4i

llPs

flo6vayeMo Oirypy opuriEa,! - Ilono 3 qeHrpoM O i aBoMa B3aeMIro repreEA'rKynspnnMz AiaMerpaM BD r MN.

tlepe3 cepearHy paAivca o, $poBeaeMo xopav AC lMN. LABC IlpaBfin6slrfi, BrlucaHlrii v lro,lo

,i!:.!:.:.i!

Aisrotsdn6 Bn,.asoro nptMoK)1Htl{d , !irverpo{ ko,la. ro npoeKui.ro nprMo$yrHr{xa e mpa-nerorpaM, Btrl{caHlIn B etinc, aiaroEar6 Frloro a AiaMerpoM

336. o"HinbKr

11106 no6yAyBarr.r

BHt HD B.: : t^D . npleoMy cH BC': BD' - CD':4R' a'. ToAt BH : HD: (4R! arl: a'.

'\<,'l ,/ A -i'

PK.

",ft?#.^

A. q noti)aoBx npoeKuii KpF"n vo p. ' .c i npo pKuji ABo\ Bra.vrro nFpopHnf\y,ripHr'\ ria

"WD' _i:_

MerpjB.

,4injrMo oa'E iB Hrx, Earpm.naA, 8,rj Ea qacrrHr.r. BinroBi.qEo ao Bi!.P'ollle]lldtr BH I HDByAyeMo BBa€MHo replTelrAlrnv'rspErx

C,fl, I8,r,,

BiApi3llr B,C, i Crr,,

8'1,, ) c,D,'

A,D,l 8,c,.

-piB:

2) qepes cepeAt'Isy paaiyca OlDL rpoBoanrE npoeEqilo xopair, rapa'Ie'lbHoi Aia' Merpy:.4rCii

iJ1:

.@.

Ai,'I],Irb npnMoliyrHr{ sa aua

rprltyrlilx{lr. Bx.or" aH nrn/16 rino eHyry AD H" Brrp:JKv

npoe(ryDaHsi 36epira€r6c.s naparenl'Hicr6 npr_ Mr.rx i "ponoplLri.i.lb lpiBFi.rb) BraP:rKiB oa Hiei EpsMoi.

79g

npsMoIly rIIi

3 po3rn.Eryrllx BracruBocreii nplr napa-renblroMy

MrB,Cr

opririHan, (pecrtrMo r{ono

aBa neptreEAu(y,'rnpHi IriaMerptr.

.[iaroHanL

LMPK rryKaH';ornrcaHnn.

Ann po3B's3aHEs 3anaqi BxiioHa€Mo rard no6yAoBr, eli y N 334, aa"li ripoBeAeMo nps Mi .repe3 Bepurlll{ rprriyrnrEa i qesrp Rora ao neperrHy 3 Ilo"IoM. APPpPIFI Bo6panieHHn BEEcalloro npaBtnbEoro tllecrtEyrE]rl{a. flpoBe,qeMo qepe:r BepiirlrHr qr,oro ecrxIryrHLrKa npoeKllrr AorrqExx Ao xona: A,B,I E,D, A\CT'

8,C., F"E, I A.E,.

-D napanenr'Eo -4C Mo rpEMy rrepe3 "orxry flpoBe,qeMo npsMi AO, CO i BO. rpErcvrlrrl{a. Toqr{s M i N - BepDnn,I IryRaroro IlpoBeaeMo Aortrqlri Ao t.ona'Iep$ ro'rll]r M i N ra roq;(s ? i R, BoHIr reperHyrbcs B ro'rqi (P € OB).

Araqe

A,B,C,D2E,F, npoe(qifl orllcaHoro trpaBrn6Eoro Illecrlrr{yrHlrl{a

ZBAC : 60"). y rpaBrr6iroMy rplrl{yrlllrKy Ilelrrplt Bnt.aForo Ici,l s6iralorEcs Toqfta O - roqlia reperlrny Br{col, MeAiaH i 6iceKrprc 11106 ro6yayBarr orErcaErii rpllxyrHIlR, npoBeAe-

Tovy ooptro{ no6vroB'I npoekui' rdKnn' 1) 6yAyror6 erirc sI{ trpoexrrirc riora i npoeliqii ABox

;,F, I c,D" c,8,,

oK = :. AO = a R. roMv -OAC = 30",

ueqrpa'!6H{fi Kvl. BiA 31ae'1n6, -AOD - 60" noBiAErrn noMy BtrrcaF]diI loAB : IABD : 30"

' I 'l

llc'

334.

napa. e,lbHoM) npoerlvBaHH; neptreRa rapanen6lricrr' 36epi-

Annyo"pEicr! re 36epiraerbcs' raerEc.n, arrs ro6yaoBr Aorlrqglrx cnopscraeMoc! r'M' qo Bc nK nptMi. nepnpHnHK)nflpHi 40 oaHi(i nptMoi.

npoeKqin BnlrcaEoro AA-BC;

rEoMETPlg Eypaa M.

1., TapaceHKoBa H.

A. iliilit:':i::i:;;:.:liit:iii'!:i:.:l

lllyl{asanpoeKqinrpEMo(yrrlr{ka,

1) BH : HD: (\2Rl'- a'z\ ' a2 - (b'z 3'): 3:: ^BPp1 2) BH : HD = (13' 12'.\ | 12':25 | 144.

i:ii:iii:i:ii:i:i:i:ili:i:i*ill:l rEoMETPlg sypAa M.

1.,

16 : 9.

rapaceHKoaa H. A.

i::!

zss

Apyra ciqHa n,roqzsa, napa"'renbHs flepsdli, neper{Ea€ Bepxnlo ocroBy trapan€nbHiii flepldt niEii reperllHy.

npaBvnbsa rplrKvrsa trpr(3Ma. PoBAinqMo I{oxcne pe6po oct{oBr Ea rpr piBni qacrrs1r' ToAi -41N1 = NrP, = P\q i +Mr: M[1 = ?,81, i 3a r€ope-

337.

Hexant ABCAB,CT

Moro @areca

MrNl Ll 8,c,.

AAIM!

ToMy

N dAlB \Cb

rKr

ntlrMiii,

AtMt: 44 = M[1',. Bpb

:4c,.

na,N, =

AranorjqHo P,Kt A\Bti PK

.;'Aaqtl

r,s, 1,4,c, i \q =;4ct. MrN,Prfrsrfr rpaBlrr6}Iui Elecrr-rlcvrEliK. Axanori'mi no6vAoBn Btlxotra€Mo s I it*Ht'o6 ocEoBolo. ToEi M\Nr MN, P$1 PK, T$t I rS (sa oellaxolo napanerbEocri npsMnx v rpocropi)' 1

B IlpoBeaeMo

ci.rsi nnoqrHr .tepe3 r{orriHv rlapv napa-'Ienblr'Ix np.sMtx. OA€p{aIIlri M:rororpaE_ EpaB]rnL'se lllecTljtiyrsa rrplrsMa.

Hr.rr{

,qrs ro6yAoBt 3o6pa){elrlrfl, oclcinblllt 36epira€r6cs rapaJe'lbHicrr' i nponopqit Hicr! Bi,qpi3(iB oAsi€i npsMoi, aocrarHbo Ira 3o6p&t(eElii rpt't&yrt{oi rlpl-rsMn noAi' pe6po ocEoB rprr3Mr. Ha

rpn piBEi qacrsE!' i s'€AEarr'I ix BiApisxaMt

BiAroBiAHo Ao Ma-nroHlia.

338.

,Aaxo 3o6paxieHHs trpaBrnbEoi

uecr*lcvrEoi rprsMs'

106 AicrarH 3 Hei npaBunr,Ev rps(yrHv rpr3My, Ar norpi6go nposec"x ciqHi nnorquHy u.p." nup, nu panenbHlrx 6i'rHrx pe6ep AAt i Cat' r'4, i EEr.

: -Acrrrt, : 4.41-FrE1 i r. a. 3a aBoMa croi RyroM Mir{l EriM1I, to*v tp"*ytn*rc" o"- I

HoB PiBHo.roPotHi. trrynaEa Or:,.Je, ACEA\CPI

npaBtnBia rpl'rKvrHa rp,rsMa'

so6panieElrE nptMoRvrHoro trapa"lencnneAa, octso3n s$oro AC iiaro'amnnx' (noaMoxyrenn'r1soSpaxeHiAoBinr'E[Mrrapa-neirorpaMaM[

ggg, ABCDAIBq|T

Hboi ocIIoBr, BIJ l -4C. BiApiaok .4C

Bfi Ainrr6

t) Anfl AHiHC:25t144, BLITaARy

trapdnenr,BoMy flpoefiryBallEi Ee s6epirarctLcs AoB]riIrEI'I Hetapater6nl-rx Bi,qpi3_ a"lle B6epira€rbc.fl piBHicrl' BiApisltiB oAsici npaMoi Orxce, no6yAona Bo6p&KesHs Aalroi dpaMiAII aHaroriqHa tro6yAo3i so6pa}lie1rll npaBrMLEoi dpaMi,4n, orrcesiii y sa.qaqi M10. RiB

ra Mipn xyriB.

qe rpa{ycsa Mipa BEyrpidA6oro lcyra trpall{4bEoro 11lecrr{KyrIrr'IKa. 120" ToMy nns 3o6paxeE$t Aaltoi tripaMiAr BuxoHa€Mo rani xpoKH IIo6yAy€Mo so6paniellss &ora i ABox Bsa€MHo rlepEel{Ar.rEynspstrx AiaMerpiB AB nn ,,l'N qepe3 rana! .anan'qv A paAiycepear.rEy nqtrivi Cr. IlpoBoarrMo xopay ^/N .ca,4B naparenbHo aiaMerpy Cr. Eya6-€&nt Bnscal{tri xyr, qo cnspaerEcs IIa xopay MN, Ma€ rpa,qycHy Mipy 120'.

AoBeaeMo qe. Oaepnisiia trprsMa 6yae npflMolo. piBEi rpaBlrr6Hi rpnt(yrEEriE: OclroBlr ii poHaMn

rlpr

341. 1)

Mti EE. AAlBlCr

rpaaj

rpaxb Bnrrcaua B &oro oalroro paaiycs, piBsi piBHocropoH!i rplrRyrHIrKr'

Oclcinbns EipaMiaa rrpaBznr,Ee

ro sci ii

6) i &oi<Ha ii

y BiAEomeHHi,4iJ I HC = AB' I BC'' nn.s BrnaaRy 2)

AETHC:AD'tDC'=1t576. cr

Or"{e, A-II4PN ocHoBa InyllaHoi nipaMiAr. JIrra€Tbcs rinr.Its Btt6parll trono}t{eEss Bepl]ral{l'r S i B'€Anarn ii s ro.rxai,v M, P i N. A 150" rpaAycEa Mipa BEyrpiIIIIIboro xyra rlpa-

BsnEHoro 12-riyrHnKa.

ro6yAyBarn Bo6pa,IreI1HE rplficyrElIrca s nyTou 150", BlrliodaeMo ri ,ic ro6yAoBr, 40 i B saBAaHEi 1), a noriM npoBeAeMo xopAy, .Efia 3'eAlra€ c€p€ArEr Ayrt MB i AytLr BN, Itre i € cropoEs r[yr.aHoro rpnllyrrrnl(a, sa Frcy ctrrpaerbcs Kyr 150". 11106

Ocl(inbnr cyMa ABox EyriB rprrKyrHt(a AopiBEIoe 90", ro BiH npsMorcyrHrn. floresyaoto B[r.rcaHoro [psMo$yrtroro rpt riyrE I{a e Aia-

342.

TaKuM {[Hov. n,rn tro6yaoBa 3o6pa {esHt.qasoi nipaMiAr trorpi6Eo: 1) no6yAyBaru npoeKqito Rona (erinc) 3 aBoMe BaeMno

Ci.rHa

Boo

rqo npoxoarrb r{epes BiAptoft Bfi i qeErp sepxlrboi ocHoBI'I Or' no Ep.aMiii, napa"renbEin Bfi (DH v BsraAnv 2)'

rroqrHa,

neperrEae

iii: rEoMErpte EypAa M. t., rapacenKoBi H. A. i-lilltii;;l;i:illiti:*Jf:i

2) .{epe3 cepeArHy f oaEoro s pa,qiyciB spoBecrn xopay, trapanerEHy ApyroMy Ai.srrclpy, ZCAB : 60'. Toqi d.43C ocEoBa aaEoi ripaMias. CepearEa O aiaMerpa - rpoektu'l BoptxnHx S. 6y4ycMo BeprHRa,lbExii Brcorll fiipaMintr, 3'eaEy€Mo Biapisoll SO - so6panceslis To.rKy S B To.r&aMu .{, B, C. S-4,8C ]I]y&stle Bo6pa,{eHss nipsMian.

if;iiltjiltittlf;l|t:i::.i$ rEoMErPle 6ypaa M. 1., rapaceHKoBa 26 vci ruP. l() M.! I

H. A.

llt

80l

Mar{Me piBHocropoHrliii rpn&vaHlr( 3i cropoEolo, piBEoro cropoHi nBaApara oclioBlt ny6a 4. flpll no6vAoBi so6paxieEss cKoprcra€MocE rIrM' qo trpri rapanenbHoMy npoeKtyBaHHj 36epiraerr'cfl na pancnbHicrh npflru/r ra nponopuiiiH:crb Binprs,'i3 o,' Eiei npsMoi a6o naparenr,Hr'Ix npsMtx. IlprnyrruMo. uro A,A,SD - ocHoBa IUvHatsoi np JvL'r. cepeA{I{a Biapi3Ira MN, MN ] AD. Ae s

PO3Atr 3. nEPnEHA!4KyICPHtCTb nP9Ml4X I nTOUl]1H v nPOCTOP|

343. 1) Haii6inbEry nnoqy

'13

A.S,N:

Sr:tl. 'o,qi

alr

,ro BoHa nppneH4xKynrpHa

',E 'b- "la\ ralil,li:

ei'a*.

uro

ot,

r" =!f;,4,

346. TaIl,

"tn

2n6+3

2) nosqa.rnMo S - cepeanlry 3) arrajrori.rHo, Ha BepxEin ocHoBi 6vAv€Mo KP \ A\D,' Ae roqfta P airarb DrCr y roMy Ji{ BiAHo eslri, i Eoslra'ra€Mo fi - cepeAzEv IfP; i 4) rpoBoALIMo ciqlii nnourrHt{ qepes naparenEEi rpsMi ArR i.AS ra

ASDA,RD|

IntllallatrPlraMa. 2) Ilo6y,qveae s Ms, i 4,4''R sr i g nepnriii qacrssi ', roqxv neperrIly BaAaqi, sHaiAeMo qeHrp AA,-E,1 McriaH uboro rpxKyrHx"a

npoBonllMo nnoqt{Hlr eepe3 npflMi Ar. AS. DS i roqH) ' Q. Bor -r rorapHo treperlrEarorEcs ro np'fiMI,x AQ' S@

DQ. QASD

l ll

'lX 'S'

npfMoi i nnoqrHx. BepErHy uux croprH.

Mo)ne, 60 ra GHaKoro repreEArr{ynspHocri npnMoi i rnoqrH rpnMa a Ma€ 6yrr ABoM npsMrrM nnorquHn o, nHi npoxoanrb qeper rot{xy neperr.rHy npsMoi i rl,'lorqr.rHr.

repreHAnKyrrpia

yMoBoro -4-4l -r AB,AM LAC, Ilp'rMiAB i-4C ne,{arb y rrorquHi.4-BC, roai sa osrralcoro r€pnenAr.rr(yr1spriocri rp.aMoi i n,'roqrl z AM ABC. ToAi trpsMa AM nep nesAlrnynnpEa 6ya6-n&i; npsMiii, rqo ,,rer&fir! y n,rorq }]i,4BC i npoxoAfir6 qepeg

35O. 3a

Hexaia

-L

Ar.

AI{ IAB, AI( IAC,

IIpnMa

sa yMoBorc nepnelrAr&ynspHa

rnoqrHn rprr{yrHanaABC, ro }oHa nepneHAr{Kynnplra i Ao npnMoi B-K, 60 BoHa nenirrb y nnol\trEi ABC M .qo

i trpoxoAsrb repe3 roqlty B. npsM01{yrHrn.

O'tla,e,

BM IBK, LKBM

Ocr{irbrcr .$f r AB i AN I AJ- ro dV L4BC aa ogrlaftoro reprenAt4 rryrrpHocri npsMoi i n:roqusr. B ToAi _pnva .t/ trcpneunHxy,r'rppa Ko)nIifr nppMiii. u:o npx/16 y nioulrHi urecrrtsyl r,{a i npoxo4u1" .repe3 ro.rKy A. Orriie, rpEMa Alr' repneEAHnynnpHa r'olx'lifi tu np'rl,nx AC . AD i AE .

353.

TecroBisaEAaHHe N9 2 1, B.

2. A-

354. OcRirLrcr AiaMerpr (pyra neperuHarorhc.E i trp.EMa neprer]A1rnyrsplra RofirsoMy B snx y roqrli reper'lny, ro sa o3lra(oro nepnesArxyrEpnocri rprMoi i nnoulnHx

3. r.

AaHa npfl Ma nepnedAxHynrpHa nnoulr.r,ii r{pyra.

4. A (ItyrE naparenorpaMa

nonapHo piBl{i).

355. Ocftir6nr rpaEi trpFMorcyrEoro rapa-qerenineAa trp.aMollyrEiKr, ao DDt LAD, DD, I DC, aofy DDt l,4,BC aa o3EarcoF nepneEA'RJrnpEocri trp'Moi i mor{oEr. AEanoriqqo, -4r l rr, AD L DC, aofy AD L DDPp.

5. r.

802 ill: I-EOMETPIg

uro nF-

349.

352, Ocfiinbrir

+. e. 5,

,o 6yab-!Koi nprMoi.

'roAj, AK I AtsC aa @Esriolo repreFArtiynnpEocri npsMoi i rnoqrFr. 3Ha.rr.rrb, npnMa Atr repneHAnriynapHa 40 6yAb-.slroi rpsMoi, rqo ,eEr{rb y nnotrrfiHi ABC i npoxo' Axrb.repe3 ro'rRy A. O'r a<e,.AK L AM, AK L AH, AK I AL.

t|t*)|",::.i|t: 2. A. 'li t:.:t!.\i.1

':iE:iiiiii

e e,

344. TaK,60 nprMa, ,poxoArrb qepeJ loiu{} neperhFy npFvor o i nnoqaFll d.

351-

iiii::"ix!: 1. r.

riil:i::!:.d s.

CO, BO

nDaMa npoxoaurB'1epe3.niibHy

roqKy .4. OT,rie, .4-4{

urycaHa niPa-Miaa

TecroEi 3aBAaHHt Ns

3a o3naEorc nepfleHAnriynnpHocri

347. TaK. rKqo

*'=

MN;

BoHa nepneHArrKynnpHa

rrorq,rEn: nKr\o AO L BO i AO

Bamnnol frxlro npaua nepneEArrr{ynspHa ao !xo!]xdu,

_ "Js

Or*ce, rop,laol( no6yAoBs li

qi€i rnoqrHr, rqo rpoxo-

AOen.aoAOIn.

.,6' srf

I 6yny.Mo MN

urlrHi i trpoxorxrb qFpF3 ro'rKy nFperrHy. OBEaIla. ,fiftrqo rpsMa, .sxa tepernirae rnoqrEy, neprreH-

z, NA=o-L=",8 222 I

9. nepneHAllryrepHicrb nprMoii nnoulr4Ht4 OBnaqeEEs. rlpnMa na3nBa€rbcs nepneHAutansp1o]o 0o nrou.IuHu- AKwo BoHa nFpcruHa. E$ nnooruHy i ncpnedA[$ynspEa Ao 6yAb-rKoi rpsMoi, nKa nerKnr!.y rnoArrrlyrr.sprla Ao ABox npsMrx asrb qepes roqliy reperrrny,

sN=q. 2' =

gypAa M. l', TapaceHKoBa H. a.

::i;::i::::: j:::::::::ii:::::::::::::::':::

::i:i;:iilili:ji:itiiiil:ii::: rEoMErPle Eypaa M. 16"

1., rapaceHKoBa

H.A. lJ::: 803

-4'8, roMv rrpsMa '4, repneHArrKvnspEa rrnoqrEi Ar43' e sllaqlrrr" repneHArltyrrsplra Ao npEMoi ABi' rlo net$trrE ]a rrolqv Hi A1'4-B Orxre' A.43rD - npsMoxyrE]tfr. napanenorpaM,60 AD I Bp, i' AD = B,c1 (nporruex' 2) rlorrpllltvrlilll{ -4B1Cr,

356.

B LCDM (ZC

L, L AA' AD I

MC [epreHArlryrspEaAo rulotqr- M rru rptftyTlrlrKa ABC, orr*'e, CM L CB i CM L AB. 1\ CB L CM, CB L AC sa yMoBoro, roAi tpsMa BC nepnestqnyaspsa go nrcr\t'Er ACM; C 2) AC I CM , AC L BC 3a yMoEoIo, roai rpnMa AC ]IepreEqrEynspna ao trnoqsEr'I BCM 3a o3]raKolo trepresArrKyrspEocfi npsMoi i nnoq:'Hld.

357.

BC-

L ABC, rolIv CM L CD,

AC =

d\6

tt/'Eiit::i.t-it].

ti;:?,!.!,ii.!'.::,

' ttl?.::i-r.!i.t

LABCT AB'!

tc");

804

npoxoAlrrb 'reppr

ro'#y

&r BD I MO i BD LAC,

90. ),,tonv

zre

s,AJ

tcMl;

+zx=,la,f=zs cM.

roqqiO, MO IABC.

BD L AMC.

S-4 = SC, ro A-A,SC piBHo6eApeHrri. To.rKa O treperrrEy Aiaronanei trapa,rerorpara € cepeA[Eoro fior{,

S,,4",, =25,44,

Ae - se, AB '[7tt, -;-----;

tE'.h' Nw=-. rEoMErPle 6ypaa M.

228 = Ja69 =

=,lua+

-L

sdaqD

roMy pe6po,4lBr reprerrAlrrcynspEe

npsMa SO reptrenArrKy_

nroqrrri rpalli,4,1tr,r,

AF ,!i".",. s*u, )+", +o,uJi -"".

- b.tE + C.

8Jt2"" .,

=--

i rroqutln

A,D.

zMA.D:4D ,tA4;

rpxKyrHhHv AB' cepe4trBa riDorelty3tl q€Erp orlficaEoro Eona, To,qi

::::t

$44 +

+16" +tE,

a Bnasurr,. ArBr

aw =Lo" 22 y rpsMoKyrHoMy CM=

^82"

365. At4 I lAr,4Br I /,r,,

kMI

T="u

-,.

MeAiaHa SO e Br{coro$: SO I 8r. ToAi 3a o3IIa&oIo treprerrAr.rKynspHocri trpsMoi nnpEa nnou{nEi .43C.

ta" + 0"

: Sr)

ABC

'lRa

'm04

B llnx. MeAiaAa SO € i Bncororo, ro6ro SO I _4C. AIla"loriqHo B pisHo6enpeHoMy rpnnyrnuxy AaD (SB

DnoortFLI A,BC.

rE6

Eoi

u" .

ZC : 90', CD 1 ,4-BC 3a vMo- npEMolryrFvit, Boro, roAi rpsMa CD reptreEAlrllyrrspHa nox{lliii tpsMin

361

. ,rE\

BDl = AD, AB,. BD

364. Ocri.nrnu

*t" =Js=s (.*l; 2\ DM = BM ='ls" +7 ='6+ro ='Es = I AM =.'E. 3" * 4" = JrB t t6 ='6a (cr,a). etr =Ji

O..J6.rn

: Ac' + cM';

9 ou=enr=^,!z'+f ="E t*t; .

6*1,

poM6, AisroHari.r&oro neperr.rsarorEcs B uto MO IAC i MO I BD. AiaroEani poM6a neperruarcrr,cs IIin rpsMnM nyroM. ToAi. AC L MO, AC L BD, sBiac'r AC L MBD.

ou sw=uE-t''

AM = .tAe * cM" = J2"";

' qe osxavae,

nR aiaroganb rcBa,qpara

3 LACMi AM'

=2J=s

363. Hexei,4BC,

a'.

a),,o*y

J6?6

BiAnosiab:1) 3147 cu, 1J cu; 2) AJ41 cM, 2b6

MB' : MC' + BC'; sa' = la' Me LDCM = MCM s^ E!'oMa l(ar€ranI'I (CM - cninLHl'ii'

LA-BD]

2) cD -'"E2' +18"

i rjlorqnEr'r.

JTc"

BD = 'ls" + 4" +12' = Ji+16+144 = r,/i69 = 18 (crr);

BC L BD, roMv spsMa BC reptrelranlcvrlsp' 3a oaHaIrorc neptreEnnkyrTtpHocrj npn_

A LBCM:

+ 6" +

.t8""

2t cD Jr2' -2, Jlaa * 9 Jrb. = 3,ii7 (cM); .

nnoquHi,4JD

360. -4JcD - xBaApar, CM CM LAC, CM I BC.

CM,:

3a yMoBoro rp$Ma d, repreEArrcyrspHa Ao nnoql'rrr A,4BC (ZC AD IAC iAD IAB. 3 LABCT AB?: AC, + BCz: a, + b,. 3 MCD CD,: AD, - Aa^; CD = JF. a, .

BC L CD i BC L AC, roMv rpaMa BC neptreHArrcynspsa Ao n.noE\*tatr ACD.

Moi

CD2 +

362.

35A.

DM'=

2,'22 o* =,14W *12" *1e _.lFr,ol+ t44+ BiAnNiAb: l) 13 cM; 2) 26 cM.

Ba yMoBoIo flpsMa

359, BC LA.B,

tEir"

DM=

g0")t

.i =JCD'+cM't DM=lc, --;+a !o-

I{i cropoHl piBni i tapanerEEi). AD I AAt, AD LAB,'toai 3a o3l{anorc fieptreEAr'lKyrlspHocri flpsMoi i nnoultrsn rpsMa.4, nepneHAlrRyrspHa rnoqr'IHi,4"4rBr, a sEaq,rrE, i Ao npf,Moi-4111' sria ret(Itrb y qin trnoulrui, Tonty ABptD trpsMollyrlrr'IK.

t6' B.Ii4 | 2s6 2

80 (cM)i SasqD 80.2=t6O

-= = ro"/i69 zl sa""=- sG11l --:=5.13-65 2 S\u,,\o = 2s^,u,o =65'2=130 (cM'z).

(cM,).

(cM,),

'BiAnosiAb: 1) 80 cM,, 160 cM,; 2) 65 cM,, 190 cM,. 1., rapaceHKoBa H.

A. lllittjt;::it::tlri:.i'.i:.ii::'!l

iialliliit:lllti-r:.iii:itii:* rEoMErpte 6ypAa M. t., rapaceHKoBa H. A.

iil:

sos

ocxinbEn EpsMa OM nepr€HAIlxvnnp1ra Ao nnorqlrHrl xona neprer{ar{r{ynnpEa rio?riEii npsMin Ilnourtiru Eona, EIo rpo_

366.

xoaqrB qepes roqRy o. 'loai O1'l . OA, A, OM

2:12

l) AM:2OA:6

BonA

'rR.

"6i

He>.an

LBCM:

AASB

Or '85. 5 l.\') fcut.

S, IAB.

Meaialra 3a yMoBoIo, roAi

CD Ao

(yrHlrnr.

MC MeAiaEa A.4JC. AD: a, BD: b, CD: c. B^A.DI AC JAD CD" =;,'--? 13 A.8Cr: BC = GD - CD'z .!; , ,( b LABCT AB' = AA'z + BA'z. AB =.tqe rBc'=.tF -," +t" -,'=,t"".b" ,"'.

Brcorai

rrolqnEr ,SC.

lpoBeAeMo B rpaEi -4BS DK ll ST , rcni DK r AB..

Y rpa:ri lBC 1

npoBeAeMo

CT, topi, KP

AB.

,-&P

2) Ipalri ripaMiAl

, -

IlryKaElrii rep€pis

S.4BC, y sKoi Bci p€6pa piBEi,

aoBi,'IEHa

ro.r&a pe6pa AS. IlosHa'rl'rMo

ruo qppe3

ro'i}

flpoxortrb

,Jo' ,

372. Hexrin nroqusa d nepneEAr&ynspHa rpsMiii -48 i npoxoarrB M BiAptuHa,4i. gItlqo P ,qoBinr,Ha roql{a qi€i n,rorrrEr, BiAMiHEa Bin ,M, ao Ats I PM, roNry PM B cora i MeAiaEa rplllryrEr]ra,4?8. 3Ea.I'rrb, M?B * piBrio6eApesun: PA: PB.

d i APB npperrienu(fl 6 no npflviti. qo flporoar16 roq(y M i nepreHnnKynapHa npsMii a sHa.Il{rr,, y nroirrEEi ?1?B qepe3 ro..Ky M npoxoAunr 6 "13, aBi npsMi, nepnpBr/,)nrpHi AB. qo deMo}l{nrBo. rrepe3

B LACMT AMt : c) , xi AoaaMo piBHocri (1) i (2)

3 LABM AIr'Iz = a' 3 LAMt AM' = b' B A-ABC. AC'z : x' +

x'. g'.

(1) (2)

A2.

a'. G'

BiaEiMeMo Bia cyMr

piB-

Hicrr, (3):

(r.

1., TapaceHKoBa H.

rpnMoEyrHnri, .4-44 t-43C,BM= a, DM:b,CM:c. 3 nepreHArl{ynnpHocri rpsMol,4,ll i nno!{'rHrr "4BC tlj]JnfixBaet AM L AB, AM L AD i AM I AC. nosHa'rr.rMo cropoHr trpsMorcyrEERa ,4-B - r,

qr.rrr, sftcioMi trapa-trerblrlrx IIpsMI'r).. SEaqrrb, qope3 ro.{Ry, .s!{a nenirrr! rio3a rnoq rorc (}, rre Mo)rcyrr, rpoxoAnrl'I ABi rpEMi, nepresAnlcyrsp_

,li: rEoMETPts 6ypaa M.

cepe3 cepeAuEy

373. ABCD

'qBi pi3-

AD:V

so6

v flpevot(yrlroMy rp/tsylHrKy.eoca Ha r-inolcHyrr . uesrpo\{ onxcauoro Kora. t M w ='- r;u ,2 Btdnnairtt: ! Jn'z + tt'z tr'

Iri rpsMi, neptrelrAnKynspHi nnoq[ld cr. IIpoBeAeMo qepes Hrx nnoqlrHy Y. IIE nnoqrlla ne_ perEe rrnoq ry (x IIo rp.EMiii .4-B C4 i B - ro'rl{u tre perrEy rrpnMl-rr( s nnoqrsolo d) Toai s n,lor,.luHi y qepcr loq*y a npo\onqrb aBi pi3rli npsMi, trepreEAr'Ikyr.spsi lpFMifi ,4-8, qo cvnepe-

Hi Ao nnoqsflu

z"'

wuP':,r'

IIa pe6pi BC cepear-rEy Ir foai "lla r BC sI( MeliiaHa i Bncora AA,BC, S( I BC rI( MeAiasa i Bl'rcora A?CS. ToAi ra 03HaKolo qFpocEAHK)nspHocri nptvoi i nroulrrHx 8a , A-KS. AJ(S - ur\kaH fi nepFpi3.

369. npxn).rt{Mo,

enep P roBlnbHa roqKa npocropy. piBHoBi4raneHa Bia roqo&.4. i B. .fl,iuro rotKa P BiAMnrtsa Bia M, ro MeaiaHa piBEo6eApesoro rpnxyrs]rHa APB e iIorc Bncororo. ToMy PM L AB. fiK6x npH qhovy ro.rna P !e ie)<ana 6 y n,loulxHi .r, ro F,ro-

npasrrblli rptltyrHtniri. Hexan

| ,tu 22 ,te

'Hex6;

ToAi AB L DKP, ao6'to

'ir. -- - ---. ,ltil:{.:.:t-:

A -

H€xan , AoBitr'Ha roq$a pe6pa.4,s. IIo3EaqrMo Ha pe6pi -48 cepeAnEy ro'rlly ?. Toai ST - MFAraHa i Bxcora A-4-BS, CT ve4iaHa i 3 'ora LABCT ST L AB, CT L AB.

LDCM sa

rodro ABMD

3a yMoBoIo Bci pe6pa ripaMiAr S.4-BC pisd' or*ie, npaBl'"'ILni tpnBci ii rpai{i

repreEAqny,rnp Ao fioro nnoE{r.rEn.

npsua C, repreFAnRy,rspEa nnorqrEi.4,BC, oj}xe, CD L AC, CD L BC i CD I MC,

Orxe,3a 03HaJtolo nepneBrt'IKynepFocd npnMol i nnoq

364, 1)

371, V MBC lC = 90",

AaHa

sn rprrMa,4-B treptrellAg(y,'Isplla

rcBaApar, MC

Bjlaq\arr,, BM: nB piBHo6eAp€EEn. OcliinbKr AiaroEani RBaApara ro.rkon O Airarrca naanin, ro OM MeAiaHa i B/cora ABrMi OM L BD. Aiamlla,ri riBa,q para nepneHAnnynnpHi: AC I BD-'lont BD I OMC B 03Ha{<oFo nppneHArKynFp'rocri npeMoi i nnoqxsx.

- MD,

cv.

Sr L43. Ananoiqllo, B MBC

BC t MC I Cr. 3'€AHa€Mo ro.lry '\4 s ro.rB.O I D(O- roqKa nFperfiHyAiaroHajei KBaA-

'IoAi MC

karr

ripaMiAa, Bci pe6pa.sxoi piB' tsi, roai B.i rpaHi nipaMinr piBHo.roporHi rpIrKlr-

367.

37O. }lexan ABCD para).

s LAou, AM = .{oM\ Ao"; AM = J4\ 5" = tE6 + % ='41 S.4BC

npflvokyrHhi:i. (cu), 6o O-4 narer' qo neErI{rL

nporx K)1a 30". rF OA R.3Bi{.r 2r S"e

Bidnoeidb:1) 12 cv: 2)

3 qeHrpoM O,

A. lili;til:li:'!il:.:;:iii:rii:;i:;ii

laa*iilt:i:di:l:li:iilii:r rEoMErPle Eypaa M.

1.,

rapaceHKoBa H. a.

::ai

807

AM, + AM, - AIf,: a2 12 rb2 A2- c2 + x2+ V2i Alt[2: a2 +b'AM = .[Vt b" . "" 3 piBsocri (1)r a' + bz cz : a2 x2' x2 : c' - b'i AB=JV-t". 3 piBsocri (2): e2 + b2 c2 : b2 v'; a2 : c' - a': AD=^lV-a". eiano,tiao'

'l7 374. 3a ]'MoBoIo y MBC ZC : 90", ZA : 3O'. CM I ABC, to(i CM IAC,CM I CB. AC : 18 cM, CM : 12 c\1. fipor,eaetto MK L ;\8, MIl - BiacraEb Bia ro.{&!r M ao flpsMoi A8. 3 MCMt A.I'12 - AC'z t'M'z: AM IS t 12'= 144 - 324 464. 18=€ Bc = Actsso'= B = 0"6 f"*1,

981.

44 a6o Dp\ a6o DC. 382. It OK' : OMz + MKa; 3)

383.

AKM 1BKM i rp{piBEn€Mo oAepfiaHi

t*i.ii!:.:.

r.t

ili!!:r,.ii:

i,rd::ii:::::'t ?:r.:.:{.:.:, '

szg. z1

r) r=16'+4=5

Bc = JAC" - AB, =

344.

troxtrra'

trpo_

'469

MBC (ZC : g0"ri AC

.4C =

= 10 sin 60" =

2t AC

(cM).

BnacrnBocri repnelr,qxftynflpa i rox{noi g&ulo s roqriu, B3fiToi IIo3a trJrorquEoro' [poBeaeEi ao nroqfin1l rlepfienalriynap i roxuri, ro: 1) repnenA{Eynsp KoporElrir 3a 6vaE-aliy ro]{rnyi piBsi' i EaBra&r, piBsi tpoe:iilii BiAroBiAaIorE Zi npoexqii piu""" "o*""l." pjBsraM noxxrlrMi n rgox noxs"rrx 6inl'Isa ra, rpoe(qis sRoi 6inr'ura.

8o8 tit

Jr|"

10cos60'=

rEoMErPle Eypaa M.

1.,

20 cu

24a

25 cM

26a

=./6?6

4s =

tB" =

t2sina'"

-12cos45o

rapaceHKoBa H.

iill:liiil;Jill:i:.::.:i::':::til!ii

AC =

=,a 1

cos

= u9,1.5s,a

=166.

s, BC : a sin d.

10.t = 5 t"rt, =

; 12.

3) .4c 8co.30'=8 =

lod

@*1.

tn = (c"t. = t@i-tE "/io.+o =zo AB =,,tEc" sC = JA6"f . (24h, = @"- 14"r(16,+r4.,

BC =

(rE

(cM);

=s 1c'"1; '=../rd-d + s" Jun*zs

sl , =.llz'

=.1r4"

nTa

= .,/6% = 25 (cM).

rpoe*qis -rox}iroi .4C Ea trnoE{nHy o.

neprellAlKvnspa'

25 cu

Ac = JAa\

nepneHA[lryrep i noxrna go ntol4l4H1|

ocEoBa

-tr" -

'EE"

(cM);

24 c\t

cLL.

378. .48 - nepreHAlrRynsp, B eRrdis [oxnroi.

BI-rpasI'I:

ocEoBa fl epn€HAI'I$v' nepreHAlrxynnp, B - AC rlox'Ina, C -ocEoBa troxfiroi, BC nspa, -

li::::!:::if:

.4J

JoK' - MK"

3) MK =,rEK" -oM" =,lts" -s"

npsMii, DeprieEA r{y'rfipllii Ao rlnoqaE'i.

= ,!225 -144 = J81 =

Ilepflell{n$ynspoM, [poBeAeExM.b roqKn Ao Aal{oi trnoq}Illfi' EasxBaerEcE BlAplBor{, qo cl1otyr{ae aally rorrKy 3 Torrnolo llnoqrlE[ i net$Itrr' Ea

' i/l

a6o

2) oM

MK,: AM, - Al<":468 x,; MK" = MB, - KB, =ZSZ (|ZJS ')"; 46a x'1=252-432 t 2qJBx x"t 2aJ5.r = 6a8r r'9J3' B rAttx: Mx = J468j 243 = J225 = 15 (cu). S 1O.

or=rlou"*ttr": oK = ,112" ne = Jl44 + 2s6 = = 20 (cM); "400

tz's 1"*r. AB -!c cosJU' Ja = g LBCMT BM' : BC2 + CM2 : I0A + 144: 252. cM. fiGHaqlrMo -4ll : , cM, rosl rr=(rz'6-r)

Bidnosidb: l5

.4r;

2\ AA1 a6o DDi

2 = J!,

Btrpassi{o l{M'9 3 rpr:,!rytF.tr:r"iB

< BC, 60 6inr,ra troxuna Ma€ 6in6lny rpoe&qirc; Marcrb piBBi rpoeKui:.

2l AD = DC,60 pi{Ei noxr"li

'[t+t'-c'; ,[, r";

^ABCt

380. 1),4,8

czi

sJa

rcrcr.

*lo-- 6J2

(cMr:

;= 6J2 t;

{cM,.

+Ja rcur:

8sin30'= 8 1= 4 rcur. 2

l"*", Br. = d rg .r. - = 6 tt,qg= cos60" =e ,l=I2,.*r. 2

385,3A48C:

ilti..:.:lillitiatlii.i:l:ii: rEoMErPle Eypaa M.

1.,

rapacenKoBa H. A.

l{:!

8oe

Bc=6 te60"=6 G=6"6 (cM). 2) .a-B 5: cos45'= 5J2 lcMl. BC:5.tg45":5(cM). ,/3 28 3l AB 14:cos30'. 14:J-. ,^ t; (cM). BC = 14 te30'= -ia + 386.

: 39O. 1) A,4BC - piBHo6eapeHufi, 60 ZBAC IBCA, aoii A-B: BC. Oc&inbKn piB lri roxnni MarorL piBIIi rpoeRrrii, ro AM : CM. 2) MBC rpsMoKyrEvir, ZtsCA: 90" - 56 = 34.. OcllinbxrB rpnlryTHnrcy rporl, 6inr,uoro ]tyra reriErr, 6inbma cropoHa, rc BC > AB, ro4i MC > MA ax noxutLa, .sKa Ma€

28J3

lcvr.

391. 1r

Bci BoEIr aaroi ro.rHr Ao n,!oqI'IEI{ Mo}risa rpoBecr4 6e3'1iq piBErx roxruux'

Marorb piBHi rpoeKqii, ro6ro BiAcratri BiA oclroBrr reptrenAltRy'r'npa Ao ocuoB rpoeRqin piBHi. Toai fM oclroB roxs,rlrx

3A7. Hexait ABCD -

nBa.qpar, AiaroEaii .sKoro reper{Ha0r}'cs B roqqi O 3a yMoBoro 1'fO -L ABC, 'toAi MO L AC i MO L BD'

ro6ro

rptn va{x{n AOB, BOM, COM i DOM npttrrc:ivr]dt' MO - 'x cnin6rsn xarFT. AO : BO : CO - DO ttIC noroB'Irlj aiaroHanefi nBaapara' Orxe, AAOM : LBOM : LCOM : LDOM 3a aBoMa liare 3 piBEocri

31 393.

6irEmy npoeHqirc.

tsq=!g=L d:45.: 'AC

"i,'o

49 = 1.1= 1: n -

AB22

a:ao"AB 2 1=1: 2 "o"o=49=! 3"6

aJ3

3cM

6cM

8cM

30"

30.

1) ,43

/Ccos3o'=

Bi,{ BepinsE ltBaApara.

3a8. Hexan.4L I ABC, KC i KB

noxi'i, roai -4C

aC =,4csin30'=

ix npoeKqii. AC < AB.60 B npEMor{vrrroMy i.4-B rprrcyrHnRy liarer MeHffIti 3a rirorenv3v.

389, 1) ,;

nepDeHA{rcynspa -4O,

voi A,4 ao n,lola'aHu. 3a BnacrEBicrm aiaroHani xBaapara -4C = aJz,

toai B

A$1

o. rt"urrr.

slo

ff;

60.

45.

(cM),

16 =

3o", roAi

=,1T44 s6="4oe=e"6 tc*t, c

-4c = .43 : cos60'= 7

60".

ra t"'),

=.tzn' + se = ^li+ tq" =.ras+1e6 =J245 =?,6 G*). 6t AB BC, 'toMy zA - C 4 s , .os +5" l1 ; 2

393. Hexaii .'lfo

LJr2

ToDt AO

D 2

i::i: rEoMETPlg 6ypaa M. 1., TapaceHKoBa H' A. i:::Jit::iiiiiil::::;.:i:.}i:i:i

tcNtt.

neprerrArrxynsp.

- BO CO

DO sn npoentrii piBH x noxx-

oAgi€i roqr(Ir. Orn{e, y rrornpuiyrEn]{a AJaD AiaroFani piBHi i ro.rkorc neperr{Hy Ailrrbcr HaB Ilin.'foni AtsCD KBa{par a6o npnMoxtrHun.

nt x, trpoBeAerux

sI( IlonoBlrHa AiaroEani RBa,qpara.

.oJzA BiAn.aidh::.

coscr =

AC 14: '-:: = 14J2

rre aoBr$IrHa llepnesalllcytnpa -4O' rpoBeAeEoro

60'

A\BPD,

r roqxx 4 nptvoi

rapa.ne,rraa nPnuiii ,4-B

ToMY,4-B ll A,B'cr. BiAcraHb BiA rp.sMoi.43 Ao nJtorlq.],Flt A$PD

A1B9

2) npsMa

14J2

rcMr.

Bc = JAC" - AB" =,112"

'ro,r.iy zc = = ",n !/.rc,

oJz

'..,- o ,----

BC41 = =-: .I:;ll)"_ ACA2 3i IACB - 45', 'toaj. BC AB : 5 cly.. = AC AB: coslbo =st f ',! . r"e r"",. 2Jz

ali

=tAc =

srncl=

rpsMin,,r' e BBrDp, rouv lai I BBrD,D BiacraHb BiA ^ DDt rpnMoi.4-4, Ao trrloqlrsu BB|DP - qe AoB]r{nrla ' rpoBeAelroro 3 ro'rRll / rps-

Js "a

6 1= 3

cla

45.

AB - ,lAa' Bc'3 = J8' - 4': J64 4vB (cM,, tr48 =

npflMa.4-4r napanenbEa

; B

\...,-...

sJz

OcKinll{lr 6irbma llpoellqiE BiAnoBiAa€ 6irbrriii no KB. xnniii, ro ltr

6cM 14 cM

:CM: DM'

ro6ro roqRa M PiBEosiAAareHa

5cM

rpr*yrHrris BtrnE' Ir

BAE,N\OAM: BM

.:0",

BiAnoqiAb: 1l ra:1''2) Iti; 3)

raE.

r::::ti{::Jililti:ra;i::.:iin rEoMETPte sypaa M. t., rapaceHKoBa H.a.

i!l:

At r

394, Hexak ABCD - rapanenorparr' O - ro'rKa reperssy ioro AiaroEateii MO nepnesanKynsp ao finoqr'IEr{ napatenorpaMa. MA: MB _ MC : MD.

Mor*nl{Bi ABa BlrtraAltt: piBlrosiAAaneHa roqlia Jlexi'lrr' y trnoqtjHi oapane,rorpaMa a6o He,lelKur6 y Riii 1) ffIlEIo ro.fca O piBEoEiMa-rIeHa B\A BepElrn raperr€norpax,a, ro AO : BO = CO - ,O, ro6ro noro ,qiaroHani piBHi. gxqo x napanenorpaM va€ piBHi Aiai'oHa"Ii. ro uefi raparrenoryaM - rpaMoriyrstF{. 2) Hexaii M ro.rRa, piBEoEiaaateHa Bi'q BeputrH rlapa' A nenofpaMa, 11lo nerr!trTr' no3a itoro trnolqlrlrolo. AM : BM : CM : DM. Toni AO : BO : CO: ,DO sI{ npoexqii piBHrIx troxl,nlrx' sqi.Acf AO + OC = BO + OD, AC : BD. ToMv -4BC' - rpaMoKvrlrrli'

3S5. Hexan -43C,

PoMi6

i AM = BM

: DM'

DO ttr' npoe&qii pislisx lloxurnx. SBiAcq BqnnrBae, D\o AC : BD. PoM6, AiaroEani srioro [poBeAeMo MO 1,43CD, ro4i AO

pilBIIi,

CO =

canoro {aBriono rpnxyrsuxa -43C: BO = R = + Ja 3 MO& AB' : AO'z + BO'i

1n:::t'i:n

,.i

fixDro

3 cM.

^r;

ro Ao - ?

AO : BO: CO piBsi npoeKqii lreHrp piBnrx noxlrnrx, roai ocHoBa rep[eHAnKvnspa ,O Kota, onlcasol"o HalRono AA-8C. tlro ne'(,lr! y cepeaxHi ri-

lED'

Ao' =

b"= 8"" 4

-b"

J4"'

AB..

i AC

ox$ni, BO

468]'

(cM).

- ix

trpoex-

72.

32,,

(5r)' 49: (8r), - 1024t 25', 49:64r, - 1024i 1024 49 = 64x, - 25x,t 975 : \gf; n2 : 25t x : 5 (t > O). Ats:5 5 :25 (cu1\t AC = 8 .5 : a0 (cM). BiAnBiAb: 11 39 cNl i 45 cM; 2) 25 cM i 40 cM. 4O2, Ifexail AO I o. A-B: AC 80 : OC - ix rpoeHaii (piBDi troxnfi - troxrni, ]/"yrr 1016 piBni npoeKqii). IABO i ZACO Miri roxsnrMs i ix rpoe&qi.sMr. ToAi

(cM). H. A.

x' 225: x, + 12r + AG - 729;12i :

BLAOBTAO':AB, BO,;AO': (5r), B LAOC:AO':ACz CO\ AO,: (8r)z

Jzro to -, .l) DU=^^ "E 10' 1/ =-'[ooz lln '-z 2 812 i:;l rEoMErPlq Eypaa M. 1., rapaceHKoBa

iOC

(oe(biqi€Er rpoBO < OC, ,tol.iAB < AC. Ilexaji r ropqifiHocri. ToAi AB = 5t, AC : 8t.

troregyslr ,43.

Do =

Bc=JAc - AB" =.t@ 4 =Jar-ae =.,48=e"6 IIo3Ea.ruMo ,C : r cM, roAi,a, - (9 - r) cM. 3 LABD: BD' : AB' AD'z; BD' : 6' - (9 r)', 3 LBCDT BD' : BC' CD,. BD, : 45 - tc,, SBiAcr 36 (9 x),:45 - x,; 36-8l+18x-x'z-45-r.': 18x : 45 + 81 - 36; 18r : 90; x : 5. CD : 5 c:|I, AD : AC : CD = I - 5 : a (cM).

.48:39 cM;,{C : 39 + 6:45 2, AO I s, AB i, AC noxrui, qii, BO - 7 cM, OC :- 32 clJ.

-b:

AI=;AB=!, aD,:2,6" 1po'.

d, l-B : 6 cM, -4C = I cM. lpoB€AeMo BD I AC, AD - trpoeKqin nepneHArxyj'apa AB na toxutry AC. 3 MBC (ZB 9O.\:

Toni.

398. Hexafi.4-Bc trpEMot(vrsltii rpt'mvrav( (zC = 9o')'

^AoD,

a c\a; 2\ 16 ct{.

BO = 15 cM, CO : 27 c}/.'. fIo3Fa.r[Mo,4B : r cM, roAi AC : (r .r 6) cM. g LAOB: AO' : AB' BO,. AO, : r, - 152. B MOCt AO2: AC2 CO,.AO,:(z+6), 27,.

- i

^l]ozq

399. Hexan,4i r

/m1. 1) Hexafr -4O I d,

V0 (c"t.

qesrp ofll{caxorc llaBliono a 4€ osHarra€, rqo roqfta O rpEriyrsnBa -419C Ro,Ia. IIIo rpe6a 6yno AoBecrg. DB = DC = a. AB

876

r:3(r>0). Bo:2-3 :6 (cM'), Co : 5 3:15(cM). ap= u{so-a.I = aGa = s 1gMy. BiAnosiAb: l) 6 c\t i 15 cM; 2) 8 cM.

iii+i:.:r.i gg7. Ijexail M e a, Mo L .t, MA: MB : BC. 'fo(i AO : BO = CO $L npoel{4ii piBE}Ix loxrngx'

DA:

roBiAae 6inr,Ea rpoeEqir. Hexai f - Hoeibitri€sr nponop[ifiHocri, ro(i BO : 2z cM, CO : 5t cv,. B LAOB: AO' : AB' _ BO'i AO' : 102 (2x\'. 3 AAOCT AO' : AC' _ CO'. AO' : L7' _ (5,c)'. ToAi IOO - 4x' : 289 - 2'x'zi 21a' : 189, r' : 9;

'^ "6 '&=6 2 t'-t' l) fxqo a=./6 cM,ro AU=B 2l

,tq.4oo

AC AaEi Doxrni; AB : 10 cM, .4C : 17 cl{-, AO Bi,qroBiAEo trpoe&qii qrx roxrnrx. Ba yMoEoo BO : CO : 2 : 5, 60 6in6rdfi troxrlnii BiA-

sHaxoAl'rrr'cs sa BiAcraHi a BiA xo'Iclroi Bep'J!'HIr rpxKyrHrKa A'BC ai ctopoF.oto a, AO I ABC' ToAi BO - CO = DO nx npoekqii piBHUx noxr{rlt{x. rpo

qeErpKora' on

4OO. IJexaia AB i

396. I{etai ro.r&a-

=Q:q-:2u"

BiAnosiob:

roql{q, ortrce,

BiAnosiAb: 4 cM.

HBa.Apar.

BeAeHnx 3 oAIIiei

iltii:l{li{iltlti;:lll!:i

iiilli:l:.ijit;:iti!::j.i;i.::iiiii! rEoMErPle Eypiqa M. t., rapaceHKoBa H. A.

Ma-

ii:ir sl3

3a yMoBoIo ZBAC : 60'. OcllinB1rlr -4J : AC, ro MJC

BD,: BI'+ po"; so-Jn'+n' =1hE (cM). AB- AF, + 8F,.. AB = . 17"- V49 289 JBaS = ta,lz f"'t. 3 "17^ABF: AB. BD. AD 13"8.17"6 24 AU=R=- 4S*n, 13 {cM). 4.204 : 3 LAOM. AM' AO' + OM,i O\t ,lr'.x,t, AO, JBb' 1A, = J(85 - l3)(8b - lJ) 3

piBEocropoHEifr, 60

IABC: IACB: Oa0" 60') : 2 - 60'. }fexaftAB:AC-BC:acur' B LBOC (tBOC : 90' 3a yMoBorc) EO' + OC' : BC" 2BO' : a"

=q, 2J2Bo =+.

Bo,

^AoB

cos zABo =

ZAB) : 45'. LABO BiAno6LAb: 45".

= tFr.ss = 186.2.49'2 = Bidno6idb: A4 c\.

Bo : en = a' - = L. ""'* Jz "

LACO sa r'a'reroM

i"E' rinor€Hy3oro, rortrv ZACO - 45'.

pdaiyc u6oro Ro,la.

S ao r,'IorqxHn

BepLUr{F r{HoroHyrH[xa, ro nox]r,ri, trpo, Ao Bepm]Itsi MlroronyrHrrr{&, piBni. ToAi piBEi i ix rpo€kqill Bi,qpisr{n, qo s'eAllyrorr, ocr{oBy neprreHArKynspa ,l4O 3 Bepmlr]{aMu Mnoror(yrfir&a. A qe o3Haqae, rqo O qerrrp noJra, ofiI,'caEoro EaBKono MHoror{yrn{rca. BeAeHi 3 ro.rRu

BircraHb BiA ro'{KH

3a iDopMvno lepoHa.

15+21+24 -P,JU: s = v5o(30 - 1b)c0 l1xs0 = 15.2 3 aE = 90,6 (cM?).

15.21

i/5!!f!!1

rt'4t

:.1:.:.

i,ltl.:.:::.:

+i...i.i.it:1.:-

"E+u

BiAnBiAb: 37,7 4) =

"60

ts g

.2.3' 2 3=

^ ^= 4.roF 6 3 so JAs - Ao'

s{orna, OM

Ba yMoBoro.4-tf

rbopltvlu n = *. 4S

Ilnorqy rpIlnyrHn(a o6qlrcnrrMo

: 32 M, OA: OB : OC = 20 M, : BM : CM,'toqt E LAOM: AM = lAo -oM^ Jro' 3T v4oo ro24 = ' = - tz,z 1*1.

406- OM

(1.

SHaiiAeMo paAiyc rto,,ra s

6 2.? = s4 (cM).

4O5. Ocllixblln ro'rKa .lf piBEoBiAAaneEa sia

4O3. Hexafi SO a d. S-4: SB = SC: 74 cM noxsni. qesrp Eona, orl,lcal{oro HaBI(o,lo AABC. ToAi O

LBFDT

:l Jrqz6- 147 Js329.73 {c\{). ,174 VJ ^Aos: SayBaxeEE.a: 24':576,15' + 211 :225 + 441 :666. 15', 21 . 576 . 666, 24 Orxe. AA-8C ronT por<v.sr.rfi, qeHrp O onxcaHoro Ko.(a ne}}{rr!, BbepeAxHi 1pr KyrHr,r(a (3a EacrdAXoM 3 reopeMr r{ocl,syciB). Bidno6iAb: 73 cM.

ABCD piBEo6i.{Ha rpareqin, AB I BC, AB:4,6ct. , BF IAD, CE IAB,'roat BC = FE = 2 M, Ar E'D - :tAn 66'1 = - 1.3 1"'1. 22 nirBai v€c Soovy nrBDkJrHApa, -4 AD - ,isMcrp. : 4O7.

zAtsD

B AABDI

BF =

roMy

90..

BF,:AF

"/i.B.

- r,ar

BiALosiAb: =2,1

FD; =

v/iJ+3 -

J4.29

.2.t

(M).

5 11. TeopeMa npo rpu nepneflAltKyJrep14

(.4, I BC), - piBso6iqsa rpareqin - 24 cvt, BC : 10 cM, B-l ,L -4, cora rpaneqii, BF:17 c}I. MO LABCD BiAcraHb

4O4. Hexaii ABCD

CD. AD

tlftrqo np.rMa, npoBeAeHa Ha nnoqrlii're' pe3 ocHoBy rlox]{noi, nepneHAl{I{yn.spsa Ao ii trpoellqii, ro BoEa rrepreuAnllyn.np-

roqllr M ao tr,'IorqllHr rpareqil. Oc$inL'rn,!,M : BM = CM : DM : 85 cM, ro roqxa

Bi.q

qesrp tco,ra, oruzcagoro EaBtiono rpaneqii. Itre Rorro

rar{om € orncaHlrM EaB&oro rprliyrrrnRa.4-BD. Paaivc .4O onncaEoro Hona 3EafiaeMo 3 MBD 3a &opMvnorc obc -S . np d. D , c cropoHx ro ryrulrKa. t1 '.24.17_2O4 l(M,). ' s..^^ -"'22 AD. BF * 3a srTa.ru'icrlo piBHo6iqeo, lpaneqii * ,"! 7=17(cM). 'lo4t FD:.AD AF:24

I HaBraft : sKuto rpnMa

Ea rnoqtl Hi nep noxrnol, ro BoHa rep trellAnl{y,lrpHa i Ao trpoen4ii floxrnoi.

reEAr.rKynnpHa Ao

s14

l:;! rEoMETPle 6ypaa M.

-'o

1., TapaceH(oBa H.

,r",. ,to =, A.

iil::liii::l:iftiil:tii:::*

4O8.

1)aIbt

2\ a.

3)otb. [ii:lii:..r.]::fili::-:{iin rEoMETPlc 6ypAa M. 1., TapaceHKoBa

H. A. :::::;: 815

416. 1) y

Zts =

A-4,8C

1aO" (Ct+ F):180" -

i trrorqsEoro sasr'IBa€rEcs Kyr Mitn rpsMoro ra ii ftpoeli_ qielo IIa trnorql{ny. ICyroM Mir{ rpsMoro

t$u,

= ,"lAB"

* BM" = nto' * e

3 tBcv cs't =,lnc\ sva

t) AM ,E n2'

4O9. Ha pxc. 221-

2\ ZBIDBi

ABC, AD L BC s& BLIcora trepreEAllr.yrraps.

411.

A.F

412, MD

L ABCD

, AC -L ,B

zBpq. rplt&yrE1'I&a, roAi ,F I BC aa reop€Moro trpo rptr 3)

L -4C 3a

reopeMolo npo

O oM:b.

i 3

,!i{r:li,:r , i?r!:4!:,

iitanl:-1.:

, ,',{:+!!1.

;'4nftr!:

ii,:qls

^MOKt

t--..- OK' -.., 1.,r t' =''{4b'-7 MK '!MO' , lu' o

=Ji

Y""

", ^,- _T*rt:]a" 22 Bi)noBiab:

="'!* _

415. V MBC ,ZC :

90", O

za" = {4s

- .f169 . 13 (cM), Jaoo zo (""t.

b76 =

!625 = 25 (cM,,

Bidnosiib:

'ft

LABC

roAi MC

: /C,

s trnoqullom rpsnyrHrlna.

MMB

AB=

2t aB=

(cM).

MMC

aa Br-rnnrIBa€,

3 piBEocri rpn-

ao ZMBA: ZMCA.

--L=2hl sin 30" ' sin

45' =J2h:

h h.2 2J3h 60" J3 3 ll2h: 2l l2hi 3l "8, ";"

iat aB=-=-=-r sin

rcM).

OD I AC i OF I BC. ToAi MD L AC i, MF I BC aa reopeMoo trpo rp'I represAlrrryrspr. Ha Bo6pa*ceHsi rocKn D i -tr' Ei,qtroBiAEo cepeAl,su xa' A rerig AC i BC, oct{inr'Kn cepeArEa rifloreEys{ O

,4-B

AC h ,tn= sinZABC = sir. ZB

BC aa reopeMolo trpo rpn ueptreB'

cepe,qslla rinoreEFn.

piE$o6eapeBHi,

Hexafi Aa r c!, roAiAC n BiA ro,rxlr - Bi{.raHb A Ao trnoErasn cr. dB noxxna, EC ii npoexqrfl, IABC r"y,r Mi t noxrnorc i trnoqr.rHoro o.

===t? 2

- nprvoRyrst{fi.

oo * szo = zo t.'1. '/i "6% = 13 cM, 20 cM; 2\ 25 cw,26 c}/..

troxui

BiAno1idb:

yrvroaoro,

419.

ll lO c]i'; 2'J 17 cll,.

AnRynflpu. Orflre. AMBC

= Jb'

J25 + r44

Jl6" +12" = Jzsa t

zt eM ' Jirt

tt'

=9=+ =-

J4 nb,2b6

414. AM L A.BC, AC L BC sa

(yrnsRiB

;AD =;.

Meniala.

,,,*

-L BC, BC 3a reopeMoro

\x AM I ABC, roAi MB i MC - noxl''ni, AB iAC woeK[i:i, ZMBA L ZMCA kyru. aKi )TBoprororb

CD' ToAj. MK L CD sa rcopeMom rlpo rpB trepneHa'{xyrtpx. MK dyRaEa BiacreHE Bi,q ro'{fiII M Ao cropoHf Cr. OcKl]lLrir aiaroEarli RBanpara piBEi i roqKoro O ainsrEcs piBno6eApeEri, Otr HaBnin, ro ACO, - fioro Br'tcora

[poBeAeMo OIf

4'18.

o. ro.rRa repernny Aiarona-rei RBa,qpara, OM -1,43C, &Baspar, ,4-B

3, I

c\4 '[n' ,24"

sri Aiarorani xBaapara, roai MO

rpn nepnesal-rlcynspl,I.

413, Ilexaia ABCD

+ 50'):90'. Toail,B

4'17- Ijexaia ABCD trpsMor{yrErx, B,l1 -l i4-BC. AB : a, BC : b, BM : c. AB L AD i BC I CD aa yMoBoro, rcni. AM I AD i CM L C, Ba reopeMoro trpo rptt a

41O- Ll ZC,DC:

(40"

nox:1']'.a, AEi ii flpoeRqri, ockinr.$ra DA I A.BC, ao BD rrpo rpr.r $epfienar.rKynspr. 2) A-Hanori.rEo 1). tB: ta0" (30'+ 60'):90".

noxrna, AC L c,, roAi BC 42O, AB:4 - trpoeliqis roxruoi AB IIa rnorqrEy ZABC F'y'r \trirx ttorsnolo i trrorqv Eoro cr. BC

c[,

- - cosZABC: AB

1) ac = acos30'=

5E;

no6yAyeMo

qeErp nona, o {carroro EaBLtorto LABC, T1A\AO : CO : R, LAOC t LBOC piBEo6eapeHi, O.D ix Btrcorn, otrie, i MeAiaEtr.

816

{!ii rEoMETPlg Eypaa M,

BO :

i OI

3)'2Bc

= acos6o" =

BiAnMi06: lJ

1., TapaceHKoBa

^t,

2t BC = a cos45. = !::i

o6, ztofi. ztI 222

t{i::iii::::i:iti:ltf:::i:.i rEoMErPle EypAa M.

1.,

rapaceHKoBa H. A.

l{I:

81?

2) Hexan ro.r4a S .4-BC, a 3saqrrrb,

i Bncora.

fiKDro

-4, I

BC, ro

M, I

BC sa reopeMoF npo rpr.

!ep'

rerlAr.rrlyrr.spr.

2\ MA L ABC, MD L BC,

.4, - Brcora i 6e1perluit]' AC

'ro4j.

AD L BC aa reopeMorc npo rpr{ repreHrl,lKynnp!.

(Br: Cr

MeAiana

sa yMoBoro) M-BC, orx{e, qen rpr.rKyrHr{Il pisHo-

422. CM

L ABC,

fipoBeAeMo CD

piBlro6eapeHnii (AC : BC). CM : a, MBC I AB,- 'topt MD I -4-B BiAcraHb BiA M

D'! Ac'

b, AC

t; li,' ,

.'z

AD'!

DM = JAM' r CD" =

^CDM:

A-B

ro.rftn M Ao rp.sMoi,4'B. 3 Mc Dt

BiAnoqiAb:

"- ="la =r

LACK

ZA:45",

O"t

=+. 2

, ,

:;t!jii:i.!

I'J DK

L-r l:la\2 -

= ,18

= Jo4

- :o

Jl00 = t0

-n

l2b+t44

= Jr69 = rB (.M).

424- l') ABCD trapaneno-rpaM. Hexai roq&a O "re*cnrs y nnoElrrEi raparenorpa-

naoo' oo = ! na =19= 22

+"F.

iioro cropiH. IpoBeAeMo M

g,"',-

JMr?

4K"

"6, t"Ll.

43 = {C,4jX8.4,8)

piBHocropoHHifi, P^M.: 144 cM. BiAcraH! BiA ro.rKu M Ao nnorqrnr rpn-L.4,BC I!].r'Enna. OcKinEKr.r 3a yMoeoro ?oqKa M piBHoBiAAaneEa

i::t: rEOMErPte Eyp.qa M. t., TapaceH(oBa H. A.

^MoK

424, MBC MO

pisEoBiAAaneEa BiA fioro cropiH. no6yAy€Mo OM L AB, OP I BC, ON -l CD, OK r AD - Bin' craHi BiA roqRn O Ao cropiH rapanenorpaMa. Po3u'rHeMo A?OC i ANOC: OP: ON. OC cnt "Ea r-ifloreHyra. ToAi APOa = A Oa 36 KarploM i - ,ore. Hy3oro. Axa,lori.rlJo, ,\/D = KD, AI{ * AM, MB: PB, 'ro4i AM + MB: BP + PC: CN + ND = KD + AI<, ao6ao AB = BC = CD: AD, ABCD poM6.

818

Tsl.nM qrrHov. 1oq<a O pisqoB aqFH_pov

poM6, M

= 16,z. rz,s = Go,s6 = o,a Bidnoaid,:6.4.M.

BiAnoqiAb: 1) 10 cM; 2) 13 cM.

Ae-

?-Z q.p, r.-t. s'-"-- = !2ap 6y ox = ?!:zsL: AD = 10 =

rcM):

2) DK= ,Js v2- "'l'

22 -et='6rl *no" =Je" ta" =n p*1. s -- = ! a6 65 - 1 .6.8 2a r".,r.

DK = JCD" + CK" =

. i/.ri!:.i:.i':. r/?.i:.i:r-.:.t

A rrnoqnlllr

p6=!sp=13=61*r.

Y ACDK:

.4in:.::r-.:.:

B qboMy

1oqtsa, piBnoBiAAanpHa BlA BiacraEb Bia ro.rxr M ao nnoqlrlrr poM6a. M-tr.1.4, - BiacraEb Bia ro.rEn M ao cropo tsu AD, loai O/( A, rb rFopFvoro npo rpn nppnps

1.4-B sa reopeMoro npo

nn""

lro

MO L ABC

rpn nepncHnrrRy,rspn.

.{acrnHi 3aAa.ri Mri AoBe,rr,

/3C, - poM6. 425- }{exafi FO trepneEAtrRynnp

* Sr,

piBHrly

BunaAny

427. ABt D

I-4J, roAi,](

SM = SP = SN

= ON = OK rr npoeKuii

t) , 'tE{- v576 49 ,527; D r = Jr6" - 12" = "Er'a tu = "Ei

(cM).

423- LABC piBEo6eApesr;rpEMoKyrHrii, [poBeAeMo C]f

y repEiii

q2a. r =1a" t".

3 clI; 2\ 7 cl{.

zc:90", Ac: BC: CD .L ABC, CD : b.

O\I =

i AO - BO' 4O... sK npoFHUii piBH aaieHa Bia cropiH !rHoroqyrHHKa. 106ro

(cM);

s'+s'

y rrnoqrEi raparenorpaMa -4-BCr.

s]{oro MHororiyrHr{fta. IpoBeneMo neprreHArRyrnprl BiA ro.ilir F ao cropin Mro rol{yrnnl{a. 3a yMoBoro BoHn piBHi: AF : B-F' : CF... ToAi BiApi3ltr-r,4.O, BO, CO.,. trepneHA]rl{ynsprri ao cropiri Mnoro(yrHrRa 3a reopeMob trpo rprr lepneHAn(ympx,

1\ DM= 2) DM=

neHAz r(yrr.apr. 3a yMoBoro

rcAi

= AB.

He ner*ir.rrE

npo3eaeMo SO l,4,BC, a ral{o,*{ SM r/3, SP r BC, SN t C, i S-K 1,4r. ToA\ OM I AB, OP I BC, ON L CD i Or r .4, 3a reopeMoro npo rpu nep-

rpn$yrHrK

BiA cropiH O - rreHrp BrIIcaI{oro Rona, B piBEocropoEEboMy rpfiIlyrH]rxy rre roql{a fepertrny MearaHa, Bucor r orcer(rpr-rc. Hexaii.4, MeaiaEa i Btrcora, rori MD I BC Ba teo-

peMoronporpx nFpneHArts\ntp s:Arra-68:AlouKr Ao (lopo ry BC, \[D - 19 c\- OD p6r')c <oia. nnrcauoro r M-Bc.

i:::.:lfliialiifl;l::ii;llti

iiil:.:i:itialfiiiiiililiir rEOMErPle Eypaa M.

1.,

rapaceHKoBa H. A.

i::i:

819

144 r8 ac=P*' t"'r. 3 3

6p= 89=-$=aJa r""r.

2J3

Bc = .,,6o' * s.r12 BiAn@iAb: 3a-

2lB

(lbopMynr satelrlAocri Mi)tc cropoEaMtr Dpanlrnbuoro MtroroKyrHeKa ra pa4iycaMr BnrrcaEoro

re ofificaEoro fioira).

s dMoD Mo - JMD'z -

Jrs' - (eJa)' - Jaor

rsz

13 1cv1.

apr treptreEAr.rRyn.sp{.

B LBCM BC' = MC' MB' :

,4D

.BC src

24'

- l5' :

24 cltr, MD :

- tG D" AD"

20 cl,r.

s Moat Aa =-L=2al sin30"

s M'BC:

576 - 225 :

Bc =.tq-e" + ee =.rE"" + s"" = J6"" = "J6. Bi7no'iab: aJ6.

- 35r -

"60'

1) Bc=a..G=a!6

BiAnosiAb: 7 ctn.

- '{AE ' AD', '[r ', Z' - ,l-S. I B, Ba reopeMoro

flpoBea€Mo.4-aJ -I BD, roai A1I1

rpr

trpo

trepEesarrKynspn.

l1 S '.-. =:S

-.--

Mi.

Itr)'I{aEa Bi,qcraEb BiA ro'rl{n .ll1 Ao cropoHn BC.

y 7s66,6s=Las=fi 22

2 ,"*,.

s*"2BDJ5J5 --=L92 a11 da =25*" =2;l.

- Joc\ oE .,6tt = = 25 (cM).

3 LA\AH.

ou.

434- Hexai\ ABCD poM6, AC:30 cM, BD = 40 cM, AM L ABC, AM - 10 cfir. IIpoBeAeMo /-K I BC, roai MK L BC Ba reopeMorc npo

=::.2.1=l tcurt.

,\H - "[A4 * Arr

(cM);

2) Bc = 6 .,6 = 6J6 (cM). Bilnosilb:I\ 4rG oa; 2) 6rG

=Jaoo-ssr=J49=?(cM). 4go. 3 MBD DB

,F{F

^tr;

=!so

s,".^=!aa,=\oc *'" 2" 2 an=!2 so sif; = sscD: Bc . Ar<i .ax =

BiAnoqiAb:

431.

ToAi'

ZABC

rc'.).

3 LAMKi MK

cr,

troxuna, BC

ro IBAC :3O"=:,4-B2

: 60'.

cr, roAi .4O : d BiAcraEb BiA - noxrui, roqnri.4 Ao rnonlusr, d. AB i AC OB i OC ix Kyr Mi){{ noxunolo i nnoopoerqii, -4O = - AaO " 30"

432- Ile\ ft AO -l

AACO aa r(areroM (,{O crpnM KyroM. SBj.AcL\ OB : OC.

3 taoB: oB.

Ao te30"

ctrinbHnn)

i ro-

alz.

BC'

82o

OB'z

i:.1::

OC'

rEoMETPlg Eyp,qa M,

1., TapaceHKoBa H.

A. iljl;tl!;!:l::l::li:i:lii1l.1:.:

^tr;.

t AK'

q0=600

(cM,,.

= zl, rco.

"44

z+'

Jroo I 576

J676 26

(cM).

EerpaBr-rrEni A&Hi:

: BC + AD, BC-AD 16+30 AD-BC , (cM). Att 23 kMJ. A! = 2 2 2 =7 7' Jszs ts J$o av30 (cM). a BF = {e.n' ar'-J;l PF

2OB. OC . coE 12O':

roBsr:Ilo 6yrs He 27 cM, a 17 cM. piBFo6i'rEa rparertis, -4'B = Cr. BC = 16 cM, ABCD - cM. MO I ABC, A, 30 MO BiacreH! Bia 1o,{Krt M Ao nnoqlfEr rpareqii. Ocxinr,Icr ro.{KA M piBEoBiAqesrp xona, Aar€Ha BiA ycix cropiE rpareqil, ro O B {easoro ! rpaneuito. ToqKa O - cepelrrEa BirpirKa. rqo B'ensy€ cepeArE{ P i K oclloB, PK LAD. A }lexafr BF I AD. Oc&ir6r{n B rpareqib Mo*cHa Bnucarr Rono, ao AB + CD

^ABF]

3 ABOC sa reopeMoro IiocrlEyciB:

,tAtt4'

435. nputLimlra. B yMoBi Ba{aqi

- ii

BiAno1iAb: 60",

qraHolo a. AA-BO

Bi0no6iAb: 26 cvr.

cM'.

Hexafi AC

.ffkrlo

9=s

+ soo = = ,li5' t 2U = ,[-zzs

s^.^^ 1rs an=1.J5

: 45'

s AAon: AB= OA =a-E: sin45"

nporrne'lrEi cropolrr trpsMoriyrsnEa.

3 LAMD AM

-Js "o"6 = '67 , u" = "tsV = so.

433. AO I s, AO : A, AB j. AC - tlox:dni, OB i OC - ix trpoeEqli, roar IABO i lACO = 30" Kyrs, sxi yrBoprororb roxturi s nno' :drl,''lolo d, ZBAC : 90".

BidnoBiAb: 13 cM.

: 15 cM, MC : 429. ABCD - .rp$jfoxyr'lax, AM L ABC. MB -4-A I BC aa yMoBoro, roAi MB I BC sa reopeMorc rpo

-f,3

BF,

oK=tPK-,=af -

iittltl::iii!ll::::{:::: rEoMErPle

z'm

t"t.

Eypaa M. 1., rapacenroea H. A. ;{li

821

s trutor<, Mo = JMK'

oK' - .tE|" r,o

lffi:\n

Biqno6i0b: 13 c\r.

"46s

442. a I tr 3a

= 13 (cM).

443- d

436. MJC - rpsMol(yrlrzi piBEo6e.qpesld: lC:9O", AC: BC AC e a' BC e a. c[, i ZBCD = 45' IIpoBeAeMo B, 1 c[, roAi d, - tpoeRqin noxl,Iroi BC IIa l1norlt4Ey r.iyr, .Erxii yrBopro€ riarer BC a nnorqnrolo s.

AllanoiqHo -4, - IlpoeKqin dnoreHysLl i ZBAD Boro i nnoqrllolo (l).

- InvKalIri

(lcvr Mirn rinoreHv

^BCD:

"-:! = y"' -4,4c - AB22

srn

437.

cD = BD = cB. sin4b" =

IpoBeAeMo

^ln

J-

BC, aoAj. OM L AB

BC 3a reopeMolo rDo

: BC : 5 cM. B rpr&yrHtrri. r(errrp r{ona, To'rKa O OK I ABC, OK = 2 rM. OM Ba paAjyc Bor.a Eoro t(ona, 'roai' KM I BC aa reopeMolo npo rpl{ rep' rrerqrrRyrspn BiacraHb Bia roql(u -& ao cropoilr A rprkyrdrxu. s r, 3safiAeMo paaiyc BnrcaHoro Kona s lDopMynl / : P a+b+c . ae p= 2

=98

1.5

3a ibopMynorc

lepol]a

^xoMt 2-5 BidnBiab:

ou'

Jr" .

a=12

(cM')

\5' = J4. r,% =.16,25 = 2,5 (cM).

c\a.

fiIlqo :]noqfllra nepnelrAtrKynrpHa Ao oAEi€i 3 ABox rrapanenbEnx npsMfix' ro Borra repneHArrrcynspHa i Ao Apyrol. ABj qprMi. neptreHAxHyJ!tpHi Ao oAH:ci nnourrrHr.r. naparerbBi. npsMa trepneHAfircynspHa Ao oAEiei 3 trapa-.1enbHl-rx

rpnMxx, ro

BoEa rep_

i ao apyroi.

,qBi nnoluu'M. oepneHArKyitpHi Ao npflMoi, napa,rc,rbRi

I o sa reopeMoro rpo rapatenbEi rpsMi ra nepreHArlrynspHv rrou{lrsv. 441. al b, oclrinbKE aBi npsMi, nepneHAr&yrlsplri Ao oAEi€i trnorqrEr, napanerbHi

44O.

e22

ii{: rEoMEIPle 6ypaa M.

I ..

roAi 3a GHaKoro.r

ABoM npsMlIM b i c, .FHi reperr-rEamrbcrr, rrrorrlxdu cr.3a reopeMoro npo napa0erEHi trrtolq!{Ir}.I ra neplTelrArxy

1., rapaceHKoBa H.

rqrEi 0, roAi a I o,3Hatlr.rrE, EpsMa a treptrenArlry,'rsplla Ao 6yAE sftoi rp.tMoi, rqo rernr{rb y rrnorqrrEi cr i rpoxoarr! rrepe3 rorn y ix neperEEy. TairM qrEoM, Il a b.

44A. 1) MA

KDiMA: KD

tr.(.r.o'loBr.rHr 6i.rH'x pe6ep napanereti:lr!'!'a,aoaiAMKD otl..{:f,o KP |DC. ostsarcoro rapare,rll{ocri nnoqlrH rrnot\:d]dLl ABC i MNP

napare"lorpaM

i M-r( I AD; a{a

npfMa, rqo npoxoar{rb 'repe3 cepeanEn pe6ep rC i r,C,.

DN,

roMi'rr,MN -

lapaxenorpaM,

' DD,IMN. Oc$inB&r rrr L,43C,rciMN IABC. 2J

AA,O,O

rapanenorpaM

(Apt I AO, A\Ot = AO). I ABC, ao OO\ I ABC.

ToAi -44, ll OO,. Ocl{inbr {,4.4,

12. 3anexHicrb Mix napa,lerhHicrto i nepneHgrKyntpBicrlo npqMuxTa uorqnH

reHArzny,'lspa

perrEy npfMoi b i n,lorqssrr d. Or*ie. b

DtMllDN, D,M

flKqo

2 s S 12).

Ao oAFi€ii B aBox napa,{e,i!ts6x rpsMax d i b trpsMoi a, roAi BoHa repreEAnxynspHa i Ao rpsMoi r. Toai npsMa, l1epreHAsKyr.apsa Ao 6yAb .sKoi rpsMoi, qo ne}I{u rb y ftnoutrjHi a i npoxoAnrr, qepe3 roqxy re-

450. 1) MN

rc,r^t.

KM =.[Eo"

/149. ABi cropoHtr oirypr Mo,{yrb 6yru Ao mroquEn, sKtrIo BoHr, rapanen5Hi. Tal(lrM qrEoM, repneHArr(y,rrpHr.{vH Ao fl,rourHHH Mo}Kyrb 6yru ocHoBU rpancqri i npol /rexHi .ropoflr{ npaBx,lbHoro urecrHKyrHr{Ka r Hc Mornyrr, aBi cropoEr rp,tlcyrtrrlta.

o="*!*o=8 t"*t; s^=JEts-5I8 5t(8 q='6 4-:z=a '2 oM

y niapt^rHlrny 3a,{aqy

2) OcKi,rbKa rnoqrEr trepepi3y i ocHoBr{ trapane,lbHi, a 6i'r' Ei pe6pa repreHAnriynnpEi ao rroq,llrlr ocHoBlr, ro Bo]rr treptrellAr.rKyn.spdi i Ao nnoqm { repepi3y.

6 cM,,43

lnorqy rprriyrHnlly aEaiAeMo

F (,qnr.

,rapnynoauya-0.

reptrerranKynnpr. 3a ritrorellysolo (BD cd,!6Ha) i rocrprM nvroM, roAi BM: BN i A,'|{BO = A-'I/NO sa riareroM i riDor€Ey3oF OB. 3 piBHocri rpukyrrttKir ssrrasae piBEicrb BiAnoBiAE[x xvtit: ZMBO: INBO. ToAi BO 6iceRrplrca rryra.43C

447. IIpsMa a repneqArftyrEpHa npsMuM c i d, .slti neperrHarcrbcrr i rex{arb y mro

AMB, = ANB,

LABCT AC

a, rouy

444. flnorqrEa o repne:rAr{EynspHa

(1,

rp'

43A, Y

i BI

446. IIpnMa a nepnelrAnr(y,lspr{a

alz -'-: tBAC = 3o".

,.It4 L AB i DN

445. Oc&in6itl' npsMa b represArxyn.apHa rrpsMt4M c i d, qo repernHarorbc.a, nnorqnstr cr, ro b I d sa osraxoro. a la, aro, roAialcr(3a reopeMoro npo rapanenbsi npnMi ra neptreEArriyrFpHy n,'loqtrHy).

Io3sa.rDMo,4C = BC: d. s MBo AB = nE * o" = oJt. B

rpsMi ra nepsesanltyxrprry rurorrlltlry.

reopeMoro npo rapanenbHi

a. lli::il{iiiliat:.::rall]:i:!1

3) B4 I ABC, 48, seperrllaerbcn 3 BBj, roMy rlp.'Ma BrB: Ee nepnesAr$yn.{pHa Ao rrrrorqr.rHrr ocnoBr{.

451. 1) CN -L AC, CN I BC, roMy CN I ABC. Ocrirrbr"u CN I BM, ro i BM I ABC. Oc{in6ri' trpsMa Br ,!e-

r$rrL y trroquHi ,4-BC i npoxoAr.rrb .repeo ro.ry B, ro BM L BK. 2) PoBB'nsaEEs aHa-.'iodqse Ao 1).

452- BM I BC, BM t.4J, roMy sa o3Hariorc neprerrAr(ynnpEocri trp.EMoi i nnorq!HE BM L ABC. CN I BN, roMy CN r .4,8C. IpsMi.4C i CD ne,riarb y nnorqrHi ,4-BC

i nDoxoAsrr,

qepe-3

roq](y C, roMy NC

IAC i

CD.

453. OK L AC, OK I BD, 'to4i OK I ABC aa osHaKoro nepreEAnriynnpEi npsMoi i rnor\tt1lj. CM lOK, tory CM IABC. 3na.rsrb, DpsMa CM nepnesAnEynspHa Ao 6yabsftoi

rpsMoli,

y rrorqrlli,4-BC

i rpoxoArrb

qepe3 ro\F.y C. CM

iCM L CN. ::::iilril;:!;iii{iii::.::.:;ii!* rEoMErPle 6ypaa M. 1., rapaceHKoBa H. a.

::,:r

823

454. ABCD

poM6, O

460- AM IABCiCN IABC, rovty AM lCN. AD I BC flR ocnoBx rpanelii. TaI|I{M .rrHoM, ABi npsMi -4-tf i AD D.noavFv DAM, qo nepernHarorscfl , lirnoBiarlo napa"lenbHi trpfl MxM

ro.r&a trep€rrny fioro Aiarosarteil. 3a $Irallolo nep-

AM L AB, AM L AD, roqi AM ! ABD treEAr{nynspEocri trpsMoi i rnoqnElr.

ToAi, ocxirbrcr ON | ,4,tt, ro ON IABD, a stsaq{a6, !psMa ON nepfiesanF(ynrptsa 6yab-EKifi npsMiii rnourlrHu .43r, qo rpoxoAlrrl, qepe3 roql.y O. OTj!J.e, ON L AC i ON I BD.

455.

AD BC

NC i BC nno]a\ dv BCN. Toai sa o3Eanolo trapanenbl|'ocri tl,;'o:,jrrr],j. DAM ) BcN.

461. 1, AM L A.BC, CN L43C,

si cropoHn

,4r,

roMy aC

ToatABCD

a 0.

IJpnMonyrnrx,

MAD I) MCB panenbnocri

I si BC Lcl, roai A, llBC. 1) .flKulo -4, : BC, 'to A-BCD rapanetorpaM nlt qorlr-

456.

Ba yMoBoro,4r

B sriiii ner$rrb iEma npsMa rosiall c I allc.

2) 3& npsMi

y sHoro

-A, I s L BC I s, to!:i AD I BC. i ,C raparenbHi.

- rapan€norpaM. AD L a, aoMy AD I DC, i-4JCD Mnfi Kt"r.

npsMoKyrEr.Ili sI{ napaterlorpaM, y sRoro € rps-

cl',

sKqo

BoHs trpoxoAnrE qepes roqRy nepernHy Aia-

rpsMii

intsoMy BriEanrcy B ErorqqEi s qepe3 roq&y M npoBeAeMo

q}IHy B i B IIin

flnoqr.rEn o i p rapanerEsi, 6(] BoHs o6nABi rlepreFAnlryrspEi rpsMifi a. 3Ea'rI-rrL, rpsMa b, slla nenirrb y [rorqulli 9, IIe Ma€ 3 rnou.iltsoro d )'toABoi cninbBor ro'IKIr, -0610 b I a. p:,,.c,2

rpaBr.rn6lra rpnRyrHa nipaMiAa, -4,, cepeAlrlill ii 6i.rEr.Ix pe6ep. -B,, Cr ToAi,4.1Cj cepenns ni:fii'- LAnfC, A,C,|]AC; &Ha,lori'{-

481

i ArBr, r{o

reperlrlralorr,cn, rrrlo-

i ,4i

nnor4rHr,r ocHoBH. i 3a o3Hafiolo napaJerTBlrocri n,rouruH A\Bp1 A.BC. MO - BEcora nipaMr,q\ ro]i'y MO I A-BC, ToAi Ba reopeMolo npo flapanenr'Hi nnoquHs ra neprleH_ Arrlynsplly rpnMy -44O L. ,BLCr.

824

puc.

2) Hexan rerep -4 € cr. qepes AoBinEEy rocKy B, po3Miqesy tro3a fiJroqttlloro o, trpoBeaeMo [paMy n, depneri4urcyJrfipHy rrJtou+rsi d (AnB. no6y.qoBy 1), a qepe3 ro'rRy A EpoBeAeMo trpaMy a, [aparqeJr6Ey n. SKrrIo oAna s aBox napanenbnr.rx rrpsM&x lleptresArr(yrspsa nnoqnrri, ro i apyra reni ii IIepIIEHAI,IRYNSPIJA. OT'IiE, A I C[.

-AasarpsMa,A€ a. flpoBeAeMo qepe3 rpsMy a sKi-Ee6yAE ABi

u{rl{r-r ,4rArC, BiAnoBiAHo fiapanerbHi rpsMLIM ,4C

AIl I

464, Ilexait a

AB.

ToAi ABi rp.nMi A1C1

rpoBeAeMo

AH Ld'

459. }lexak MABC -

nerir.rrb tro3a trnoqrmoro a (prc. 1).

npfiMy b, fiepneriannyrspay RpaMifr 4. qepe3 flpfiMi, qo neperusarcT6cfi, AM i D npoBeAelro mro-

458. Hexa* [p€Ma b i nnoqrjEa cr nepreEArriynspEi rpsMifr a. OcRinb(tr rpsMi a i D nepresAtrKyntpEi, ro cepe3 rpnMy b Morrclra DpoBecrI'I nnorqr{ay F, nepnenAr.rEynspsy

i rnoq&Hn).

3 roqKz ,{ orycu.rMo rreptrer{Ar.rliynsp AM Ea Aesxy rpsMy a nnot\rr{u p. .flxnro -4n4 ,L C[, ro uyriaHa nprMa no6yAo,

ll Molrie nencTtr B nnoq maa,re , a6o BD l e.

Ga osHaRoro naparenEHocri Ep{Moi

463, 1) gexan ro.rl{a.{

ToAi .4-BC,

Erx rapan€nbEa nnoqnni,

3a o3Ea&orc flepnerraurcy,lsprrocr! EpaMoi i fino]4trR r a I AEF. 3a reopeMoro rpo rapane,'rr.Hi rpsMi ra repreBAnrcyrapuy n.roquny, ocriJll'xr.r a t ll c i a t uP, ro b I AEF i c L AEF.

yMoBoro ,4-B

ffFirio npsMa reptrenAr.rRynspHa oAEit 3 ABox DaparenLEnx trpnM{x, ro BoEa reptreHArr'rynspsa i Apyrifi. Toli AE t oiAF I o,

qepe3 rorr&y

rrpEMorcyrrrrrE sr{ rapanetorpaM,

rrotrlrH.

462. OcxinbKn npsMi a i b rapanerbsi,

puxyrExrr, y rRoro ABi rropoHH piBHi i napatenbBi. OcRirE&lr .4, L d, ro AD I DC, 60 DC € o. j' trpoxoAl{rt'

r. Toai ABCD € lpnMlrii Kyr.

trporrrne){-

poM6a.

Toai ]l4,4B liIcM Ba o3IIar$Io napa"!erBEocri trnoIIIfir, 2l Al',1 J- ABC- CN I ABCaonv AM ll CN. ,4, I cD nR rpornnexEi cropoEn poM6a.

ai.

"p"*il,oC, trapanenorpaM. ToAi.ABCD".pa"rerssi:A .4, -I c, sa yMoBoro; .Bc |

roMy ,4.M I CN.

nn ll co s*

sa yMoBoIo; Ilnoqvlra, rpoBeAeHa qepeg _ qi npsMi, rcperrEae rnoq&try d no

i:i:i rEoMETPlg 6ypaa M. 1., TapaceHKoaa H. A. i:ji:::i::iiiri:+::::iiii:::ii:::

r.roqnlllr

IIIyKaHa nnourxHa \1a. ncppruHarr qi nnoll]aHr no nprMrx, repnesAr(ynspErx Ao npnMoi d (osEar{a repreEArrRynspHocri trprMoi i rrolqnsn). 3sjrcu no6y4oBa. Llepei Eprvy d upoEoalrvo Ari AoBiJrEHi rnoqnH*r (r i 0. y Roi{cHii iB qnx nnoqnE rpoBoanMo qepe3 ro.rEy .4 EeprreHArrKynsp Ao spnMoi a (m I a, r? 1a). Ilnoi.qnHa. flHa npoxoar{rr, eepe3 npEMi ln i r,

:tliitilial:i,taiii:::i:lt rEoMErPle sypaa M.

1.,

rapaceHKoBa H. A.

{it:

825

465. Hexnii AA

iioro cFppnnHs. 4aHrii{ BirpiJoK, C IlpoBeAeMo.4-4r Ic1, BB\ I d i CCr I o. ,4,4r, 881, CC, BiAnoBiaso BiacraHi BiA ro.ro( A, B i C Ao

474,

npeMi d4,. BB t att leaar" B o.4Hifi n,loruuHi, rka neperrlra€ nnonllrHy cl tro trpsMiii ?trBr. AAPP rpaneqia (,4.4, BBj), ocnirhl(s C cepe-

Avta

A-B

i CC\i AA.'to CC,- .cppaHn ii}lis rpanF AA +BB

rrii: CC'2= 466.

BbbMeMo AoBin6Ei lotrl(n

A i B B rroqltHi Cr, napa-'lerblrin rro[]x]ri & i napairerlbHa rnoull'Ei p.

1) finorqnlrrj nepe-

IpsMa,4J rexurb y nnoqrHi

rnHarorbcs no pe6py CD. CD L ADD, ro*ry

IIIyItaHa BiAcran! - BiAcraEB MiEr napare,'IbrrliMlr lrnorl'rHaMu. Is rorrox A i B onycrxMo neptreEAErcyn,rp r A-4t I BB\ Ha lroquEy P. A{, BBr rrx nBi np.sMi, napaier6Hi r,rotqrHi F.

Tor'

npfl

y,.or p

AprcDiADrcD. TIyEaHI,Iii IIyT 1,4tDA.

| i aa ,re}+(drb B orHii io .r'"i. r-/rd 4.4,4,4 nporHnex{Hr flnpntsu flapa,lc,lb

A-4

lri, orlie, qe naparerorpaM. 'fal{l{M

.rIrHoM,

IAtDA =

Mt - BB'.

45'

nnoul

,4,

Ha. npoBFreHs qpppJ

DC, BC

BiAnoqiab: 1\

DC.

OrHana.

n"pn"Hdu|gtspiu,,tu, fl{rlo B)1 .ai)n

H}rM}r ,IroorB-

qcpca npqM), qep Fq.[xRyreDH)

aoap]

nepteHArKynnpEi, ro 6yA!.sl{a rplrMa, rqo BnacrlrBicrb. Erirlo aBi nroq]Il nexHrb B o!Hri:i J r/\ r n.pnerrnxHyrflpHa io optvo ix flepeTvHy. n.pneHnrRy,'rnpFa Ao Apyroi- nnoq]IH]r.

ZSMC;

2) SNB.

(.\aJ;

cM:

3) 3,3 .\d.

npoxoAr.rrb 'repe3 6i.{Hi pe6pa (y6a, repneHArlrynEpEi ao oclroBlr, roMy sa o3rraRoro reprreHAnRynnpHocri nno$\\1sv BBIDt I ABC.

477. 2) llIyl{aEtrnllepeph 3 AACD AC = alz. So^,"," =

3a o3nal{oll) rreprreHArrriynnpEocri

472. TaI{,

sa Bnacrnlicrro nepneHAtr(yrspHux

nnoqtlr. qe

"'tE '

rE'

Be3niq. IpoBeA€Mo '{epes ro'rKy,4 rpnMy AO, nepreEA IryrEpEy nronlxni d. 3a osEaEoro repnesAr.rkyrspEocri rrorqr{H 6yAr,-nKa rnoqrFa, nrca npoxoatrrB ire pes npsMy,{O, neptreEArRynspr{a Ao rnoqfiHr ct. 3a BracrfiBicrro repneHArrrlynnpF'x trrou{rB, EltIIIo Ari

tr,roulsH nepreHAlln]L

n.apEi, ro 6yAL sl{a rpsMa, rqo ne,Ilrr6 B oAEiii i3 s'x i nepresAl{Hy,'lspHa Ao np€ Moi iI nepelu'y. nep PH,DxxynrpHa ao ADyroi nnodrllHr.

n,'Iorqsll.

473. [prMi a i b MrMo6i]$11i. Bi4craH! Mis ErMr

AC AA, =

npsMo{yrHr.r(,4ArC1C.

478.

479.

471. Tas,

ix crrinbErii nepneEAEty

nttp AC.

926

2J2

476" Ci.{Ira trnorqrsa

nepemuHanmbc,c, l]a3rBa€r6ct{ Ilyr Mir{i rlpnMtMr, ri cnL,rbHoi roqHn nepneH4/t(y,rtpHo no ,1r r r\

f (uro io -vHa npoxoarirb

t;-

a ':

Bdno\ob l) I "M:2) 2,2

nnoqxH . 1o ui n. oul/Hr' -epnpH4 KyntpHr.

47O. 1l

a sin q.

t3r so - 6 sin60'- o u" lJa t""r. 2

13. nepneHtruKynrpHi nnoul4H14

ABi n,lourrHx liro€ 90'.

ZCOD : 90", 60 alaroHari l{BaApara,4-BC, nep-

45'.2) 45'; 3) 90".

2t SO- 4 sinii'

BiSnaBiAb: 45",135', 90", 90'.

EAmo ttirt ntoutuHan , tlni npoBFAcHxMx

I ool r oD. IlIyliasnii 1ryr ICOD.

OO,.

L ABC, 'toEL OOt I OC

t) SO=2 sin30"=2 -2 = 1 (cM)i

BK t\ CD.

Dr -6.v. YMXBKB AK:AD- KD:AD BC= 21 15:6(cM). prBHo6FApeH/; npPvoky,Hrii, AAr\ B 'to[y zA: 45', rB : 180' 45" 135'. :\i.iitiii: '"i:n!!!ii:

ro rpsMiii

Ornie, Erylia€I,Iii l{yr

475. SO: SM sin qt =

npsMoEyrHarpaneqiE.

IIpoBeAeMo B-K 1,4r, rali I(BCD rrpEMollyrHl-ilt.

oo\

,/aaD:454.

BC.

pepisy,4,4rCrC. CCl I AtsD, aovy CC1 I AC

ZACD.

nptM' AD t BC. r,epetv"c,

rJiorrrxlry o no npflMiii DC, AD

ABCD

3) IInorqr}]II I1epepiBiB A c{ j. B4D1D llepe'rn-

icqLCD.

BiAcraEb Mirn napanen6ErMu n,'IoqrHaMl{ BiA Br6opy roqxn IIa onHiii 3 s'x.

467. AD L ct, BC 1 a. roMy

2t CC1 rp.sMa neperrEy rpaEi CC1r,, i re

it::: rEoMETPtq Eypaa M. t., TapaceHkoBa H. A.

440. 1) Ocl(ift$r ZABD

ilti:r::.rti:i1::'li:tutii

"1'B

90", roAi

I .r, ro npnMa.4-B nepneHArrriynapEa ZCDB

: 90'

npsMin

Br,

!1o ,'le)(Irr!

3a yMoBoro.

:il:ii:li;iii.:.rlttilft::ii rEoMErPle Evpaa M.

1.,

rapaceHKoEa

H.A.;i.& azz

ToAi /l| : o - BiAcranb BiA ro.rxr,{ Ao trpsMoi treperDsy BiAcraHb Bi! ro'rKn A Ao rrnorrnHr o.

npoxo,qr.rrr qepe3 trpsMy -4-8, roMy 3a oaHarcolo trepreHAt(yr.tpEocri rno' [p€Ma C, nexnrb y n'1oqv Hi c, i repneHAlrl(ytspHa rpEMii B, neperlrIIy rnoDInE ct i p, snaqarE, 3a Bnacr{aicrto reptreHAr{RyrrspE x trnoElrrll C, f p 2) 3a yMoBoro.AS L d. Il.norqtua p npoxoAr'rrb cepe3 npsMy.4.8, a sHaq,lrE, P -L C[ 3&

Ilrorqr.rsa

rirE

o3rraftom treprreEntBynspEocri

3a reopeMolo rpo rpr-r rlepreEArtryitrptt 48 L CD. AAB.4 - nprMoKyrHr.rfr. IABA.= I t(yr Mix nnoqu-

IIaMr.I c[

nnoq}ls. D

4A1. CD L ABC, ror:Iy CD L AC i CD I BC. nnoqr.rHr 3C, i .4C, repersHerorLcs tro trpsMifi Cr, q[Mn rnorqtrsaMx. aop'j. IACB - r.y't M\x< 8a yl/loBoro ZACB : 90', ro6ro nnolql'Hu BC, i,4CD

482. fpad $y6a

Hexai? -4,8 rqunra. A e 0.

OtrycrrMo

ffyRaHa BiacraHE,

ip-

4aai n:ro_

A.4 = 14 srn60" = 14 '2

sm9

rr'

srn

3a vMoBob A'8 = 2.4,4,.

Biinoeidt:3o".

IpoBeAeMo BD

BiAno6iAb:1) 20 (lni 2)

4.,6

3\ aJ2

c]y',

i 0 - tagi trnoqrgrl, -4 € p. OrycrrMo 3 ro.rKtr A flepreEA rcynsp .4di Ha n,'roqmy s i treptreHAr.tKynnp .A.B sa trpsMy CD [eperl-rsy rJloqlrs.

486. Hexafi a

828

i$:l rEoMETPlq Eypaa M.

1.,

repernsy IInoqrF.

sino, 44 - 1, , AB 2

36..

a c[, B,

BC), AC e d, B e d. siAcraEb siA ro.rlir B no

^ABK

Ar{ =!AC 22

- AK"

=!.

rzc" -

ffi{

r:tf:::iiiS

BK -4. ^aDr "i,1,=!4= 'l s" -a' ' J4 10" -r2' 28 ,14.2o' -24"

i#Hr{

-144 .1256 t6 2 16 16 16 l. _ .^" Jl6oo - 576 Jto24 32 2

J400

Bidno6i0b: 1) 30"; 2) 30".

V MBC zC :9O", AB: c, AC : b, AC e q, B e fipoBeAeMo B, -t ct - Bi{craHE BiA rorrRr! B ,qo nrolt\It'lrl o.. BC L AC aa yMoBoro, ro,qi ,C -L AC aa re-

489.

{cMr. cru;

peMop flpo rp}r neprerrAr{riynsp}r . IBKD : <0 - t<yr Mitrc fiJrolqr.rHoro C[ i finolqusoro rpr{riyrHr.rlia. OcKinL&{ : piBno6eApeE ir, ro K AA-BC - ceperytHa AC, AD DC s& rpoeKqii piBrrrrx troxllnnx.

10: != 20 {cm): --!L 30" = 2

s as= sin,L=a,!=a\6 45. J2

cr'r.

4Aa. MBC. piBno6e4pen fi lAts:

,48 = qin

t3 t1€ 2t AB-sin u:=u,f 2 J3- 3 -ov, t"*r, 60'

4 4J, cu; 3) ?lE

i repreEAn Rynsp.4,B Ed trpsMy

BK = '[AB'

rpr neplle1l$uF'ynttp',AE ICD, MBA\ -

= 7JB (cM).

sia roqltn A 40 npsMoi reperlrEy - ai4craau rnoqnH, .4-41 Bi.qcran6 Bi,q roqKn A Ao rnoqsrr o. 3a reopeMoro npo rprr repreEArrKynttp$ A\B I CD, aop.i IABA| = I nyr r.ix nnorqrHaMr a i p.

roq&r .4 DepneHArRyrsp /-4! Ea trnoqlr-

3a reopeMon rpo

cNtt

Toni AB

a sin q.

AeHi rnoqrlarz, .4 e P. .OfiycrttMo B ro.rKn .4 repreEArrRyrsp ,4Ar Ha n,loquHy

lleii BiApbolr aopiButoe pe6py xy6s BiAnosiAb: I\ a.i 2\ at 3) a.

485.

487. Hevai, s i. P

ix crlinr,soro rIp.{MrMu,4C i Bpl 3) BiAcreHg Mitrc - IIe AoBnrrfiIa leptrerrArrKynspa Ei,qpislla, qo 3'€AEy€ Torfin neper[ny AiaroEaneft ocEoB xy6a

Oc$inbrcn B tripaMi,qr SABC Bci pe6pa piBEi, ro A.4SC i ABSC piBsocropoHtti. Ocrcinbxn M cep€Arna SC, ro E]l4 i l-'!f BiAnoBiAao Meaia-En rpxKyrHtrxiB BSC iASC. a 3ltaqlrrb. i B,rcorl'r. BM I CS, AM I CS , CS - niEis rep€rlrry trnoqtrrr S,{C I SBC, roAi ZAMB ttyr Miflt uxMn n,'iorultHa-lt{n.

-4-,4!:r4B sin

Bilnosiib: lr 12

MrMo6iJ*snMIr

484.

nepreHAr.rriynspHi.

483, AC L a, MN € c[. fiIlqo.43 I MN, ro CB I l]4N 3a reopeMolo npo rpr treptresNnynttptt.'IoAi /ABC - riyr Mi)n nrorqstraMx o i B.

1, ,4,{ =24 sin30'=za 1 tz (crvtr '2 t; 2r ,4,4., = 8 sin 4s" = 8 !^' - +"E G$t

ftBa,qparlr. 1) ToAi DpsMa.4-4r treptreEAv l{ynspEa 4o rrnorql-rElr ocEoBlr. a orrrie, i Ao rp.sMoi AB. AB L BC. "IoEi BiAcraEb Minc qe AoBr* rsa ix cuinEEoro trepreEAul.yrapa MrMo6in I'rMn npnM]rMr -4.4r i ,BC AB. AB : a2l Bpr I AAP' rol{y BPr I AB\. BP1 I CCr. ToAi BincrasE Mi*r MrMo6ir(lrl-rMr qe AoBxIrHa ix crdnbEoro reptreEAnRvn€pa BPt BPt * a. trpsMsMn.ABr i CC1

rlnoll1rlr,,4,4, ryrntrr

TapaceHkoBa H. A. iiiii:.x;:i;ti;:::.:i::it:i::liiti

fps nepneEA4&ynsp[. Orrxe, ZBCD = (p ICyr Mi'Il rlnorq,Isolo

opeMoo npo

nno-

ulutlolo TplrltytHll$8.

i{nali*ilit it:iit:iili rEoMErPle

Eypaa M.

1.,

rapaceHxoea H. A. l!.;i

429

3AAac: ac=

rt BD

b'.3MBc:8D = Jaoo zse j-= rz j

'lAE A," =ir

Jzo - 16/ sin30"

2t BD=Jto' 8' sin45' ,lse

BD=

a.B

sinq 'c'-a

sin,p

o ,"*,,

1016

ooB 3) cc, =::l:

u\vH ABS L ABC.

491. SABCD - rDaB{,Ir,Ha ripaMiaa, .'l1 i N BiAnoBiAHo cepeausr 6iqlrr.rx pe6ep S, i SC. Toai MN | ,C.EIC ce pe4Hn niEi.s A,SC i MN I -4-BC, 3e o3llarlom repnes' Ar.fl.iynlpHocri rpnMoi i tr,'IoquHn.

Bianoaiab:

Ocnirhrcn ro.rna M piBnoBiAAanesa Bia BepEIITE (Ba{ paa^ ABCD, ro ocEoBa nepneHAr&yrspa MO, lpoBeAe Horo ao nrronll{Ht KBaapara, € qeHrpoM Hona, ollncaHoro

493.

1oqtsa ncp.rxHv .4ja o'

I ABC, a trnoqnEa,4-4{C npoxoazrb

!r48.

B3o lii: rEoMETprq

=oJ2.

tcM).

[) sJi cra;2) 9"D cu; 3) 11rE cu. iABC: l nepneEAr-rnyr.Epgi. ron\v[i ABC iAD IAB, D

<r^ApafiB ABCD n

ro\\ AD ADr DD, ,l\E AD' "G'LCX 3a"Jz. 2l^.ADqi ADr I ABC, AD L DC, roMy ,Dj.D reopeMoro rpo

,.-):. \' Y 40. " /-. - - " V qepP3 B npeMi MM, i Nv. nepnelr' ^ ocHoBu.60 Epoxoaxrh Arxynsplli Ao ocIIoBn M 4g2- 1) CM L A.BCD, 'to.l1y CM )- DC I CM I BC, ..'a 14 1pe' ./ I -8( D xyr Mi)l{ 'no ur4HaMx B( i D.M.ABCD DCM MoKyrHr.rH.roMy-aCD-90".Or){e.n,lourxHhBCM' n,/ ) d. "r----1 nepneHA/xy.lepHi. 7 nroJL?,{a DC\I A\4 2, ,,lc L AB|'D. / )/ qcpe3 vB nP'MY MC. A/ npoxolxrb -,/, I I ","',,'". n!,o|Uu{a DCM nPp-,-/ .,t,,/ | n.uar*y,rrpn" nnourxHi ASa lpqva Da niHiq i{ D nFperuHy. Ar r D( 3a yvoBorc i A, I DcM. //' /Z lhorynua ADM rpoxoanr; qepes rpaMy-4r, ornie, Bona /,/ / nepnenaN"y:tspna nnou{lsi rCM 3a oasakolo repneEllr -)t- / /// riynrrpHorrr n. orqxH. eUB M

.4'A4C

rFopevo0 npo rpr{ repoeH4rxyirnpr. KMA P lnyKdHu; npp.piJ. Biu nepnpH4 KyntpH/;i

/,i '"').-'-\

.neplletlArnyn.tpHa

nepneHAlaKyntpqo.ri nno_

1lJ2

fIpEMa.4, rejr{r.rrE y

MM, L4-BC i NN, -L,4JC. Toq$r Mr i N, ne}larr, Ha Aiarosannx xraapara.4JC, (AIrB. I& 437). Cfisa rrrroqnHa neperse ocHoBy no lpsuiii MlNr I MN. 'lo\i M!\ IAD i MtNt LCBi MK IAD i NP ICB sa

nroqrma

495. 1) Ilrorqrrr:

flpoBeAeMo

A8a

Lu=c.u=!ae=!. cc. =.lcu' , r., =.[rV= '2'{4J22 ,^ t; ," t; lt (a'2'2 ='"t' = s,E t"rt, 21 6'1^, = l9!a = 9u[ 1"r;,

OcKij"nn.i,rFo njourrna npoxoarr6'r€pcaBucor) nipaM:_ fia 60 f ABC\, ro 3a osHarloK) nepnesArKvnspEocfi nno_ A

n,rour Ri

45'. .4,8

rplrllyrElrl{iB.

notrIuHa nep€pi3y npotoar.Irb Sb. Boua neperanae ocHoBy ro rpsMiii AO, sna B cBolo qepry reperrsae pe6po BC E roqqi r. M,9, InyRaErii

qepes np.aMy MO, ro

piBHo6eApeHi, ro ix rocrpi Kyrrl AopiBHro cninbHa rinoreHysa. Toai 4,4-8C : MBC. CM i CtM Brrcorr q x BoEr Ainsrb ix Ha ABa rpnMoRyrEi piBEo6eApeHi rprrRyrHsriz.

494. OcKinbllr rp]{KyrE r{r npsMoxyrEi

49O. Hexaii S. ,BC - aoBirBEa riDaMiaa, SO - ii Bltcora. qepe3 pe6po .4,S i Bncory

sareii IlBeapara. 1) Ocltinbllrr MO

nepnerrArrr{y

nspnocri nnoqrE, 60 trpoxoAr.rrb .repes npnMy

.1;

O -

nnoqrHi-4-Il4c aa BnacrnBicrro nepDeHArrr{ynspHr{x Dnorqvu (60 ltD t A(' sI{ AiaroHard r.lBaApara, a niHi.s reperr{ry reprerrAr{xynspnux rnoquE /,,t4(l "4.C i ABC\.

ToAir,'rorqrsaB.\1rtreprenAuRynspnarnorql,Ilri.4-Mc Br.

zlz n*r,

J18 s': sin60' "lqq "i=t, "i -oJa r."r.

HaBKono kBarpara. Toqxa

2) OcKirblin rnoqrHa,4MC repneH,qHKynsplla rnoqrsiABC, ro llp'Mn til) r, t)I(,1

Ar.rliyn.spEa

:l---"'' o"'-,

rpI, nepreHAnxynspr. 'aii;,;:;;.;;;".

cD, JcD' DD' Ja' t 2a'! $a: als. AC=aJ2, AC, = aaE, CC, = a..tE. MCC1 piBHocropoHHifi. ZCAC|: 60". BiAnoii}b:1) atE cv;2) qr6 cu; 3) 60'.

3) Po3rnnHeMo AACC,. TaI|nM .rr.rHoM,

(tI

f P. I P, AAt - AA, - a, llno[\v]la A44L c. AC uyriaHa BiacraEb. A\AA a - Kr;alpa't- roa. ec = ali. t) Ac = 4\8. aE = 4.2 = 8 (cM);

496.

Hexan

P.4 e a, A

npoBeAeMo .441

2) ,{c

5a6

Cx,

,4-4,

(€M).

Bilnoli'b: 1\ 8 cMt

5J2

cM.

trnoqnHr.r d i B reptreEAnKy,rrpHi i neperr{Harorbcr tro npsMin c, ro ocKinbKn rpsMa AC net( rE y nrolqr.IHi p i nepnel{Alrlcyn.spHa rp.tMiit c, rc AC t d. AHanoriqEo, ocnirErclr B, € cL i, BD I c, ro B, t I. ToAi B, L AD (AD e F\. B MCD (ZC :90"tt AD' = AC' + CD' AD'z:d'+c'.

497. Ocdn6lr'

\zD 901: AB v Ar' s9' uf, ' Y . . \ AB=Jz"*E"*tz" = ',6Jre + ra+ = "aas = rs f"*t; D AB=.1r4'+g\6' ="62e +oa+s6=."G?6=:o rc'1. 3 MBD

Eypaa M. t., Tapacenroea H. A. i;.:-.it:i:::*tliiiti;:.illil

BiAnoqiAb: 1\ 13 cM; 2) 26 cM.

:ii!:ii:!!:i!:iii:i,:iiii:iii;ii: rEoMErPle Eypaa M.

1.,

rapaceHKbBa H" A.

:ii;i:

831

tt p=2JfiJg=

BB1 i AC M{Mo6iriEi qe AoBlr{IrHa ix cnin6Horo nepBiAcraEr' Mi*i EnMn seEArrr{yntpa BOt BBt L ABC, s:da.;j',fl', BB1 L BO' BO I AC tlx Ei^rcaani rlBaapara.

498. 1) npsMi

s*"

=.,1i5e5

as;

25)(45

- 36r(4*

=Gsuo.9.16 =ao'3 4=360

(cM');

no=Leo=! o"E='i'. 2) [poBeAeMo rnoq]rEy qepe3 cepeAr,IEy

nu=2 *fo =zo pe6pa

2l p

,4-4r napanenl'Eo ocEoBi. Ils rrolqrl]a nepreHAlftyr.spEa 6iqHr-rM p€6paM (N 448). nepepi3 - KBa'qpar, piBlrr.ri oclroBaM. BiE nepertHa€ AiaroHatE Br, Ky6a

B ao!r\l

3a osEaxolo nepnelrAlrEynfipEocri flpsMoi i nnoqEHt' ' crinbtrzi neptt]!. a\aroFiani rcBs.qpare Bepepi3y. TaxIrM'rI'EoM, MI{

K. MK L AA\

MK I BrD

resasnvnsp rp.sr'{trx

i Elr.

-t;

MK=A('.-. Bidnoqidb:

-4.41

z) ""E ",tE 2 |

.4'B

21 rl:?'L:'i:ll: i

:i!!:;Ji::

116

5.2.5=

r"rvr.

-LLE-256. 11

= .1144 +

"Xp

b)(p

1 Aj'e 5.,". :AC BM, 2b

"),

cu.

trpaBnrEsoi - rpaHr, Aesxoi croposa ocsoBn, trosHa.rgMo Al = a.

nipaMi,qr,

oK - iioro

r. ea vmosoo so

pa,qiyc

Ia.

So a. tso , ur"rn-2to-. ' OK= 2t a tqo _-;-:-: ll r=-; ".2-E = V3; tP-60' 2a 2.13

zr'22a ,=!: tua=!-2=1: o=45'r

s,o ("r1.

sa tso a' -''zJs==;Ji ql=30". -:: 2 3a iJ 2JB

3t r

BidnosiAb: 1) 60": 2) 45": 3, 30'.

5oo. Hexan -4-Bc - aagnfi rpuxyrslrli, 'repe3 croposy "4c tftoro rpoxoanrL Aes'ca nnoqrHa, Bepustra I Ee sa-rexll{T6 qift nrolqllEi. [por"A"*o a t"p-ar" -8 nepllelrar'IKvtrsp BO Ao tutorqla:fr1, 1BM IAC, roai OM L AC AaIroIo nrroqrsa reopeMoro rpo rplt lleptresAlrRyjlsplr ToAi aBy6=I-xvrl{il,{ lllyHasa siAcraEb Bi'q roqrcr'I B Ao trtorqsEr'' IIoIo i lrorqlrlloro -4-BC. BO SsaiAeMo Enorqy rpaxyrH*rlra .4llC aa ibopMvnon leposa:

s,^" =.[p@ -

cr,a;

3 a-so,ll:

=9-15 =tz r"*r, =-!U J400 - 225 20

3Bi!'RA

rEoMErPlt Eypaa M.

502. 1)

Hexan

1.,

(rr

IpoBeAeMo -4,41

.qo

fl"'loqrH

A e s., Ae g. i AA, L I BiAcraEi BiA ro'rlln

Ilroqr.rEa,4ArA, reperrHae nnorqr.rrlr cr i P no nepneaar-rxynspHrrx npemax .4'C

o="*t*".

A,c.

llornpnnyrHv t( ,4.4jC,{,

2Sw.

2.;,t;;io-b\tD-,\ !sing S^fOM: BO= BM ',1:::

f^ .. t6 15 y" = '?,

t,l Ib,- ---

KC'JCB,-KB'

\) ro

caHoro B ocuoBy.

Bidnosidb:11 l2 cM; 2) 9.6 cM.

832

60"

sa reopeMob rrpo rpr{ flepreFlAlfirynsps, lryr S.KO : Q - r{vr Mi}K nnoE saMn ocHosu i 6i.IHoi rpaHi. ueHrp koJia, BnI{' OcKi,lbxa nipaMi,aa trpaBnnhna. lo roqRa O

j as\ nc' ' ia tb'. CB: AB' = AB , KB. KB = M = -!._. Ja' t b' rc

sin

501. Hexan ABS

sa31. ,as =

(cM);

2-=z(i s*=tmer -28x27 12)121 =,,t1r7.2.15.n=.tE-s r.s s.z.l=so (cM,)r BM=1;o rs {cM):

BiAnosiab:

npoBele{o Cff I AB.MC I fK.aov.v Cl( cnin!Elr* repfleHAlri{yrap MnMo6ixsrx Ilp.f,Msx .A-B i CM i Bj,qcraEb Mit+t EuM .

LKBCI

;=10

MC nepneEA xy,rspsa Ao 6y!6-n1(oi nptMoi. oo ne,{(urr, y Enoqxsi ABC i cpoxoryrL qepes rounv C

Bo=20.sin30"=20

25 + 12 +17

ao _ 15

499. Hexan.43C - Aasnfi DpEMoRyrE,rfi rpnHyrHl{K. zC: gO", AC: a, BC: b MC LABC' toai DP$Ma

(cM);

fipaMoriyrsxK.

Ac=JA+*,\e=.tE+b". 2) Hexai

srno.

rapacelKoBa H. A. t.itit:liilll:lili:.:tlllt$:i

firorqrH ct i p nepernEarcrEcs tria riyroM 60". -4, I d, -4, : a, i AB L B, AB : b.

npoBeAeMo

AD i

A.B

BiacraHi Bia roqKr.r A Ao ruoqr.rx a

ililt{i:i;itltti;:.il:.:;i:.ffi rEoMErPle Eypaa M. 27 vci

rtrt

loE1.,c.

1.,

rapaceHKoaa H. A.

i1::: 833

flnoErusa, sRa rpoxoAr.Irb qepe3 trpttNli AD i Ats, treprleHArKynspEa nrlorqr'IHaM d i F Ba osHariorc represAnriynspHocri n,'lorqrE ToAi rnourwra.4,B, repreHArliynnpHa rpsMii c reper Hy rnoqrrll s i P. C roq xa ix rlepea]|jfiy, ZDCB Kyr Mini rnoqlrnaMlr o i ts (t{vr q). P$rnsEeMo Artr BpJ rnocri npecteHlrs B r,'Iot\u'li ABD. IpoB€aeMo

BC i

Ilnoqrrna y, .ar{a rpoxoArrl qepe3 trpsMi-4r4., i BBr, MicrHl r' I'l^l'1tr,,h 'l ir. o,, rrltr,r " Arrb .rep$ ro.rlin .4 i B. IIIyEaEa BiAcraHE - BiAcrar$ Min xprlMoro I I rl ,rr,rrrn 'r. ' y. IIpoBeAeMo qe oAsy Ilnorqr ry, .m'ia repfl€HAunvnaptsa Ao npflMoi c i rrxot'lrtrrn y AC,{2B, yrBopeErn niHinMr neperlrEy qiei nnoqrHn 3 r,'lorqrllalIn o, I i Y. ,

DPIIAB,AK I PB, rcM'y PKAB rpsMoKyrlrt,lft. KP_AB:b. ZCDP : 90' - I, ZKDA: 90' - ZCDP : 90' - (9O' 9) : q. 3 MKDi KD : AD cos q : 4 cos q. DP:DK+KP:b+acosQ.

,\8, = J4e t BC =.1i"+r4' = J4s+576 =.,6% = 25 (cM). n cM, roai B,f : (25 - t) cM. 3a B,lacrlrBicrro Bncoru, rpoBeaeHoi 3 BeplnrIIrI, DpsMoro Ryra: CK': A,K B,K, CK' : ,(25 - n). SEaiiAeMo 3Ha-relrrl.tr,. 3 LA,CK| CKz = A,C' - A,K' : 49 r'. 3 AB,CKt CK': B,C" B,K' - 24' (25 - r)' = 576 - 625 + 50:t x'. Ma€Mo piBHsEHn: 49 t'' : 576 625 + 50, - t2,50, : 98; rr : 1'96. Orxce, A:r : L96 c.l,', B,K : 25' 1,96 : 23,04 (cM). cK, r,96 23,04t cK ,[Lg6-23.04 1.4 4.8 6.?2 lcM) HexaiiA,l(:

DP l'+dcoso 3^t DP, CD=-= sin I sin A Ac

-.[AD\a"

.flxu{o

Bidnoeidb: 6.72

Bi1cmaHb

: 60', to

J""

- 4b';irbE .3"" 4

z.tE

z1E

*ffi

ob{3 *

* d .'

b" .

503" Hexan,4-B aaslrii Biapi3oR,.43 : a Ae d, B e P' trpoeHqis BiApislca'41g Ila flpoBeAeMo,4-4, I p, roAiA,B Kyr Mii{r Bi.qpi3EoM,4-B i nnonnott:,/":dy P, zABAt: 45' urvnoro 0. Asa;rorrqno ,4-B

nnorqrEolo

3 MA.B. A-B = 3

^ABtBi

. BIAB 30'

BiAcraHr' Mini oAHieIo 3

naparenbHo oeptUiii rpyry nptMy

qrx

np€Mrrx

kir

AD,

A](

Ilryxaua BiAclaHb.

Y LABD: BD ,fAts -

AD' G' + o - .,6+ :o = ro rc"l. Btr: r cM, roAi r(, - 10 t (cM) BAABKAK':AB' BK':64 ''. SAAKDAK2:AD' DK':36 (1O X)'. Hexaii

IlpupiBFfl eMo oAeprKasi BlIpa3n: 64 - t2 : 36 lOO + 20]' ,'i 2Ok - 12a; x : 6,4Bff:6,4 cM: AK = $4'6A = J64 4o,% = 183,04 = BiAnosi1b: 4,8 c:,'.

4,s

(cM).

5 14. OproroHanbHe npoeKryEaHHq

Mi){{ Biapist(oM

c[.

^t;

ABcos45'=:l:. 2 1a

ABsLn30' a -

44 = 'FP" ^AlBPt

BiAnBiqb:

tnunro'in Huiru npsttLuttu

n,1ourfiHorc, opoBcAFHoro qeper

npoBerFMo.4-K

!\ J"\E;

ilr

t:M,

5O5. IIpoBeAeMo nnou{r\ly BB\Dp, Bosa Micrlrrr' np.'Mv B,r. Itpgl..a AAj rrapane"lLHa rnorqlrHi nepepisv BBp1D, 60 ;,1, A,a'. roli ui,u"tag6 Mir{ rpsMrMr .4-4' i B,D eopis . ar Hrtle BiAcraEi Mix npnMrMu -4-4r i rnosInsolo BB,r1.

.flkrrroa:30",ro

Bianoliab:

I A,B, BiAcraEb MiJn nptrMom c i flrorqtEoro Y. LCAzB't A,C : AA\ : 7 cM., B,C : 84: 24 cM.

-4r LP.

B,E

lapanenbHe npoelrryBall'l a Hast\Batort> npa tLo x V m Hutt, a6o opmozo{anbHunt, aL1r\o rpfiMa l, aRa 3aaa€ narp.sM npoeRryBaHlrs, n€preHAlrl{ynnplra

nnoqrlli rpoeRqiii.

t, " -\z t

509, TpI{XyIIII'Ii i

510.

AaHrrn BiApi3oE, A € c.,B€ p. EpsMa rleperlr IIpoBeAeMo.4-4, -L c i BBr I c, Ae c Hy trnou{lri{ d i P. 3e yMoBoIo ,4A1 : 7 ci', 84 - 24 cM. lposenemo.4-4, I c i BB" I c.

Eypaa M.

1.,

rapaceHKoEa H. A.

1) CepeauEa pe6pa CD;

2) roqlra trepernEy Aiarosanei rpaEi 3) pe6po BC;

504. Hexan.4-B -

s34 lii: rEoMErPle

Bi,qpisol{.

-4-BCD;

rpaEL ABCD;

5) rpn&yrHllli -4CD.

liiliit:ltllliiitl:iii:

tlt 2',7*

i::ii::iil::l::::!iit:.:li rEoMErPle Eypaa M' l', rapaceHKoBa H.a.

li:i

sss

511. 1)

TaK, sKsto nnoqlrHa rcona flapanenbHa nrlolllnEi npoeRqiii.

.lo

3) S," .20 cos4s"=20::=1OJ2

2) TaK, flKqo nnooltHs Rorra E.pnpHAxKynspHa nnolrllBi npoeRuifi. 3) Tall, y saranbrroMy Bnrla,qlcy.

512. B& L

cr,

B4:

AB,

- rpoeKcis " lAu' - BBi = tE" b.

BiaptuKa

Bidnosdb: 1, l8 cM': 2) 36 cM?: S)

cepeAHs

tiHis

rptIrcyrEIrlca

1) -4C l BA1; BC: BBt AA1:8 - 5:3 (cM). AC:APt=4cM. , =.tEA + BC" =.rT6 rg =.Es = r

-4BBl

'2'2

2) BC L

BB. = 2CC,.

l0- 12 -rr,"nn'. t ,=!AEA 222-

IJ!=14, x+8:28;r:20(cM).

2) raK;

6. Hexaii 8Br

-L c{,

roai BB1 =

Jr," -

BiacraHb Bia ro'rKn B ao

Erotqlrsl

c{.

15"

J6r5 -

517. t)

- cos30"=24J3-,8:z 2r S,e 24J3

2) cc,'22 =:(14 =

BiAnoqiAb:

836 tit

oo..

o+).

MoJ&e

6yr!{ sx

Ba -A.4r,

ro Fararrb-

(cM).

2 cM; 2) 3 cM.

neperulla€ aesxy n,'lorlzHy tr. ! s, roai AA1 I g,B, . rIronrlrHa, EXa npoxoAurr, 'repe3 ui napa-'lerLsi trpsvi, reper sa. Biapi3oK

EpoBeAeMo .441 -L

rnoqrEy

B B1

ro rpsMii

41.81.

Ac tqE - Bt = lZE nBB,- Ali

{cM?l:

rEoMErPte Eypaa M. t., rapaceHKoEa

C,h' .7

Po3u.nHeMo Ans 3pyqEocri ManroHori y qii rnoqrHi. npoBeAevo Aa ll ABl ao neperuHy B ro'rai c a np'Morc BB1. Y AABC ZC 9O", BC BB1 + B\C = BB\ + AAI ArB\: AC'

lcY'z):

cepeaE ,riHir.

6irLuri, raK i MeIIrIIri l,AA l. Birnosi,Ah. orprrva€Mo: CC, ;lBB 11

520. Hexafi

CrK

=;88,.

|I cc ;no 6t ;a"2rcta\l

cos e.

S"" " 36 cos60" = 36

,riHis. cK

cc,.cK cK 2:BB '.t"",'..2lo+' 2' Hrorcu'r

finoqa oproroEenr,soi [poeKqii MsororiyrEnKa Ha n".Io1qmry AopiBEroe Ao6F&y *oro nrouti Ha HocnHyc xym virt tr,roqxflolo itlHorox,"rHlrxa i trroUllrHoro rlpo-

: S

cFpenHs

OcKinsnn BiApfuoK BB1

= = zo (cm). "4oo BiAno6iA6: l) 16 cM; 2) 20 cM.

eEqii: S"".

Y Y M.ArBr:

3) Hi.

= J256 = 16 (cM);

ABt = cB, =

Hexan -4'B

^ABBtt

:::::j**i: Air i Ca, - BianoBirtio opoeKLrii cropis A'B i CD i:ili:iiil-, rpdxyrHtrRa-48C. ;l)-::l.i*:rl AB. .IAB, - BBl = Jaz - b, . ,j.;:i*ilii ocninbkri aA,8c piBHocropoHHifi. ro cB = .43, 'x :::*:i-:*l npoeKqiipi8n,rxnoxsn'rx. ili:ilii{ \ AB\ = cB, Jzo'-rz' =Jsoo-1aa= 2)

rz 1"*1.

cepeAr.rHa BiApis&a A1Br,

BiAnosiAb: 1\ 11 cM; 2) 20 cM.

Ta&;

AaHlrii BiApisoK, C - fioro cepeAtlra. L rJ, Cq L s, ,ro!:i AA,ll BB, ICC,. vci rapane,lbsi rpsMi, nto neperrrHarcrb rpsMy .43, ne-. rcar! B Eero B oAr{ifi rnorq}rHi. IIs Dnoqlrlla neperuHae nroul$sy s rlo llp.sMirl,4rBr. 3a reopeMoro Oaneca Cr

B4:2.11:22(c[r-

5'15. 1)

"Eu

IpoBeAeMo.4.41 -t cr, B 81

BLAnosiAb: 1) 14 cMt 2\ 10 cM; 3\ 22 cM.

s1t.

BiAnMiAb: 1\ 5 cM; 2) 12 cM.

519.

t\B\:2.7:14(cNt; 2)34=2.5:10(cM); 3'

A4;

: BB,, rosi

(cu).

: AA1- 84: 15 - 10 : 5 (cM). BC : 4Br: x. BC =' ='tq* - Ac =.lls' 4 =.lT6s - % =

h 1\ .Jd' b": 2\ ..

IpoBeAeMo c!. C 513, Hexan.4,B - cepeAfiHa:A3. - Aanrin BiApisoK, Ae a.,Be CC1 I cr i BB1 1 d. IJnoqrGa, rqo rpoxoAnrL qepes napa-rrenbEi rpsMi CCr i BB! neperrHa€ nirorqruy d ro trpsMifi AB1. 3a reopeMolo @a,'leca CCr - cepeaHn nitriE MBB\. CC, =

cm'.

518.

aa.=!sn.=b. BiAnnAiAh:

IorE

'43.

4'. 1) 3 AAJaI: AB, 2) Hexan C cepepulla AB. npoBeaeMo CCr 'L cr, roai CC1 ll 8Br. 3a reopeMoro Oaneca C1 - cepeas' Ha.4,Br. ToAi CCr

lcM')).

H. A.

ii,ilillil:l.t:ail:j::itti*

i:jiltt:llililllli:.:lt:.riii:::;, rEoMErPle Eypaa M.

1.,

rapaceHKoBa H. A.

fi:i

asz

- Ee 2) -4c - !60L

roo = zn (c*); t zf = "6zo '6zo = tz t*l* 6f = Jtoo - zra = 'Ett =

524. 1,

Bi0no6LAb: 1) 24 cM; 2) 12 cM.

a"a n€preE[rRynnpr. ao oasiei np.sMoi, AlBr npoel{qin Biapi3fta : ,4-B !]a r,'rorq{Hy o. IlpoBeaeMo AC I A,B| AACB' - npnMolcyrHtIlc. AC 4Br

521- AA, I BB,

trr"

ZBAC:q'r]/"Bi.IrroBiatsi. 3 LAtsC AC = a cos q.

1) ,4c

= 12

cos

60' = 1,

r'"""r0'

522.

no.rcHeHHn

t' eB= .qB

]

.os6O"

.E = 2's.

a"6 (cv);

4rE

cna; 3)

Manrosos ArB. Ao

aJZ

:l:rexan

!ii:.:. ': !i: i. :i.ir1:+:

ABC

aa}1uii

(x. ToAi -4-41

B/-

'rb

cr.

HexaitAc:

b, BC = c.

838

cos

cM'z

zzJz

(}t'z

cM'z

32 cM!

60'

30"

60'

21-cos60'

zt.z

60"

45"

t'.r,

u alz 5* 4 2

3r2

s* - -90r, :^ ,1'# ^S

6 q

s..".

-"+'=a-',p' t6u2 r.''r,

36.2 t8 1SJ3 - ^ {c\{ .. _ = O!/.J

cos30' 4. J3 JJ

t) l6'/2 cv | 2, 6'6

cM'.

SM,!,., = SM,. cose flrorqy rp1rnyrE]rxa.4-BC sHaxoAtMo

3a q]opMyro]o lepoHa

t, '2 o=13+14+15 =zt s-"" =rD(r1 13)€1-14)(11 15) - rti 8-, 6=13-.T4.rJ ,.3= 3 7 4-a4 lcv ): Sj,q. =Li4 cosdO" 8q 1=42 tcv t. o, - 7+14+18_11. '2

szz.

',sI

coso =

ii::: rEOMETprg Eypaa M. r., TapaceHKoBa H. A.

t r ali z 24"'z

Bionostdb:

BilnasiAb: D g cIv-,16 cM, 25 cM; 2) 8 cM, 6J15 cM, 26 cM "os

rr 2)

ln' tL ,/qoo t qq r zse te r.*r, A,B Jtb +2o "lrrf, 4oo = "68 zs r,t, 2) ,4,c = !fi' - 6' = v[ao 36 = ,6+ = a (cNr); B,c = tE4" 4 = .1576 - 36 = = e'/is t"*l; '6+o s?6 4,8, JrO - 24' v/ioo = \6?6 26 rcvr. S

s"','

,[sc - ea: "F x.

B,c =

60"

cMz

^A1BP]

^BB. 3^A$\c .4Bt=Au=.tF+S. D A,c=J15" -n' ="lizs-tu=Jat=s (c*);

.S.

96 cM'

s scoso 32'E"os.15' zz,z !-=n rc* t. s. 48 1 : o:ttu'. 5l c.sro=r=-= s962 ,\q = 4c1= ,t4 sin$'=aJ2 526. 3 ' z

4 ,.Mtl

Ha nnoqlrEy

A{=,F. /4

cM'

rpIlxyrHrK. IIpoBeAeMo ,4A, i BBI trepnetsAtifrvn,'ptr ao : a BiAcralr! BiA rinoreEy3s Ao nrrorqrHl{ c[ A]C

3^AA.

6aJ3

2a cM'

s64 l. coso=r=-= o:bu" s1282 S ,u ,"',, 2r S s.os{t= 64\3.os30"=64/3

524.

= BBr

npoeiiqii EareriB

1) cM.

!!9 "ul ' e r"'rcos30" J3 Bidnusid": l\ 8 rM'i 2) 4 cv: 3) 6 rv. rrorqvHrl

I GM).

rr /R 52g.

,, "o",=4@=@..:r0.. '242

I =4.2=8,"-t, - | 212

242

525-

1"*1,

L. AB=4= cos9 cos

s 6,a11g

Y*="A

BilnosiAb: 1) 6 cu; 2)

", "".'

Bi1nosiAb: 1\ 6O"i 2) 45"; 3) 30".

3) Ac=16 cos45'=

362 . - 6s', =t4 = Q, = or", = 19 =

"o",

(10

,!:i::lltiltiliiili!:ntil:ri

i::!!:itilliJill:;ilfiiiiii rEoMErPle Eypaa M.

1.,

rapaceHKoBa H. a.

:lt

83e

s*" =rE(21-?)(21

1?)(21-18) = rtl 14

,,1}, 8'sin30".os30' 32 i "." eJr t"",; 2: 22 -t; u't; q"6 s, = 8'6 cos45'= "vo^ = rcrv1. '2 Bdnozidb: t) 3 cv i 2) 4.5.v'r 3; lv6 rv .

4 3=.tTl r'7 4.3=

3) s

=3 7 2'[2 42'2 {.M':rr s*,!., 42r2 cos45" 42'2 @=42 rct'r. 1?+65+80 -

3l D=-=61:

s*" = Jsl(sl

1?)(81-65xs1-80)="Er.ro

- 288 cos30'=

s!44c,

BidnoBidb:

288

& = ]la"E

ol=g'a s=288 (cM'?);

s=;.4

MicrnrE rpsMy MM1 i Biipi3oK ,4'B. .(ns Bp) rsoc?i posrnsHeMo ManloHoK y qiii rlnolr{xHi. AA1 : a, BB\ - b. Tocria M Ainr.rrb BiApisoK AB y BiAHomellEi m : r. Morinrli nBa Brananl{'j.

cv i 3) taq'6 .t-.

42cM'lt 2l 42

6=12

(cM'9);

=12cos60"=

n ;=6

@*\,

s=;10 8'2

BiAnosi.Ab:

szs.

LAM

2) q

' :;al:.:+:. ,.

"t.i:{.:.]:

-; =

= soJt

BiAnoqiAb: 1\ 60":2)

530. SHafraeMo

oAr.IH

;

i0v5

(cM,);

'2f)2

415-:

45'; 3) 30'.

n**o,l-,y, MB=

is xareriB aaltoro rprllyrHrKa: o cos

zrE 19

{p.

InoDIa aaHoro rpI'IKyr-

]=r'a

rc*'1,

lsnaz11

.t; .t;

2l S=' 6'?sin45"cos45' 18 ;

s,=e cos60'=e ;=a,5

:'z :,r. fipoBeaeMo.4-N I A,8,. A,AN B, : BB1 N\ = b a. M,Mt : NB1 : a.

trpf-

a, ro(i BN

MM,.

n i m.ro noBroplaBullr MrpK]BasHE, orpxMacMo:

uu, n(b-o\.

uu.

3(25

zt uu,'

10\

rn(cM):

-lt 9 ,"*t, MM, ro 9

r9(cM):

3t29

(cM): -ot +u3+5 I 6 rcvl: MM- 4 + o ro 5t2o^- 41 5 16 uto uu, ro rcu)i MM,-4 t lu- 14 (cM). '88

532- Ilexaft ABCD

!r1

BiAnogiAb:1) 16 cM a6o 19 cM; 2) 10 cM a6o 14 cM.

84O

I M \Bt

LABN 3a ABova r.yraMx.

eo":

sOJ' J' : o : '602

cM,);

a' sin 6o'co" uo" = r.

S, = 2"6cos30" =

AM BN m(b-a\. Mtl =oI Y P.. *r, ' MM, BN AB

uao

:scosq. q . s=1o 22 "o. o "irr o = 1 a' sin cos cr. sl 1) s

AA\

-6 rcMtiMM ro-ti 1l MM"-2L2: ^10)-Ll! 2+3 5

812=4s t..o'): -"o=*19-

;.6.10\E

cM'z.

cose=$.

q =;.b"6 a=10\.6

{cM-)r

1i 6 cM2;2) 40 cM'; 3) 54

q=j44;

1) s,

a0,6

Hexa AM : MB - m: n. 3a reopeMoro @aneca 4M t MoKyrsrxi, NBr

s. aolE.osa5"-ao'6 f =n0,"*r, 6'sa r.*'t. 3) s-l eJ3 8 36.6 t.,,r't: s, =govs .o"eo'=46 2)

Bj,qpi3ox - ,4-8. Toqra M dane,{curb Biapisxy.4,B. IpoBeAeMo -4-4, I cl, BB\ Ltli MMr Ld. 'tonj, AA,11 BB,11 MM,. Irorq ra, ff{o npoxoArrE.rep$ rapa-lerLHi npal{i AAti BBo

k,i."\.

528. Hexan S - rnorqe poM6a, S1 - nnollia iioro npoeKqii. s!: s cos e. aoai s = +dtd,i

531, AaIIrn

"Z:=9,""'1,

{cM'?}i

li:i: rEOMETprf, EypAa M. r., TapaceHKoBa H. A. 'i::.xif{i:$lti:!::li:ii:ii

IABC : 60". .toal DDt

poM6 si croposorc a. - €AaH'ri s. flpoBeAeMo DDt I a i. CC1 L .t,

-4-B

ll CC,.

ADt i

BC\ rpoeftqii

cropiE

,4, i

BC IIa

rJ1oqully e. ,4rr = Bq, 60 AD = BC. Tor,i LADDT: LBCCT sa RareroM i riroreHy3oro. SBincu

DDt: Cc,,60 DpCCI - napa.ne.norpau. Dc ll D,c,, DC: Dq:AB: a,'roarADj: Bq: b. A O.Kinbxx ,419C 60". ro MCB - piBHocropoHsi;r: AA - BC. ToMy Ac - Bt^t - b f,R npoeRaii piBsrx noxr. rnx. 3 CC: = BC' BC: = a' b'. ^-BCC1: poM6a repneuauKt,nflpHr i roqKoro neperrHy Ai.{lacoHani

g naoa I no =!1, oB = J AB, Ao, \. 2)

BD=2OB=a'l}.

lit:ritlllit::liil::iitltii: rEoMErPlc

EypAa M. 1., rapaceHKoBa H. A.

til:

84r

LDD,B D,B =

siarouiao:

533.

ABCD

.[nn" r)4 = Ji."

Jr'" .

b" .

AalrLIi trapanenorpaM, AD

flaparenorpaMs,4SC' ro:,d'-lri AC,

b.Eo" +b".

lpoBeAeMo BBt

8D,:10,5

1," k

AC\:13,5

a, BC

cM,

BD,

cM.

- rpoekqis

AiaroHard

46,25

- S, a nnorqa poM6a I s s ;4d,: s d'sind cos,P =; .r.""n. s's .

536. Hexan nnoqa qorzprxyrEnria

1l S=

(cN1\.

lca,t.r"(n + n\b

ril:::

=az"6 t"*,1'

ao".

I n.

Bc = \EE" + cEl =

: 4:

,E + zo'

100

: cos

"lEzr

I =

r"ln O. E

a5" = 100

l00rE.

1oo\E Lo6 = 150 (M'). BiAnoqiAb: =L50 M'. TecroBi gaEAaHHq

Nsl

cepeAt\aa AB.

rEOMErPlg 6ypAa M.

^BcE

s38. nnonra aaxy:

(m + n)b

BC Ha rrnoqnEy cl,

BE:AB

5J17 .1,06 = 21,8 (M). BiAnosi1b: -21,8 \a.

Earera - trpoeftqit &yr Mi}r{ llrMn. ZCBCI : 30' lpoBeaeMo CM -L .4-8, roai CIM l.4B 3a reopeMolo qeprreHAnKyntpr. . aMC q txyKaHui npo rpx

roAi BCr

442

6a'f

:9 M, CD : 4 Lr, AD - 20 ttr. npoBeAeMo c-E ll,4r, roai CE AD 20 AE: AB - CD:9 5 (M\.

535. Hexa; y LABC lC:9o", AC : BC : a,'roai. ZB: 45" (v flpsMorcyrHoMy Pi8so6eapelrovy rplrxyrHxr.y rocrpi Kyrx AopiBsrolori' no 45'). flpoBeaeMo CCr I 0,

MeAis'la,

537, AB

H -i{, ,o, ^y#"' :+

AC MO, 2) 3 L(ici ]l{ nponopqii CC. AMt=t

(cM,); s1 =s'sin60'=

Bianoaipb: 1) 6o"t 2) 30'.

aRitrcf _AMBMABm = ''aMDMCDn r) V aACC' sa reopeuop oaneca.4Ol i OtCl: n

Bscora

s=i.16.8=64 t;

Eatr\ BD.

^^F -",-"il'=f,:

LAMB N LCMD sa aRoMa ftyraM'r.

Cll4

(cM:):

,4,B t CD : n t n. - rpaneqis, ,rr I d, MO1 I o. ToAi "LC1 EpoeKuir aia.oHani AC. BDt - npoer(is ,iaro-

Mitrc nnonlrrHaMn.

8 9=36

ix IlJlorqr'

IIpoBeAeMo CC, -L a,

51, Iryr MiJn

'2= 62 sin30'= 36 18 tcu':t: 18 i p:60'i cos9= =

(cu). 249.

-4b'.

45" .

534, Ijexail ABCD

xyr

aa.=!sa=!.

BiAnoqiAb:

\,661 = 19 (cM). Bidnosiab: 17 ct"1. l9 c*1.

^AMo,-MCC,tr4o,

J' - "J' 22

cC. a aJ2 1 =::O 'cM22J2:

Br'

1) !L'

^Baa.''22

L a, aoIi, AB$|D rpoellqis rroqnHy q.-4C, - npoe(qi.s aia- A

pariB AiaroEanefi: AD2 + ABt2 + BlCt' + Cp' : AC'z + DBr' noslla.rrrMo ans Bpt-rEocri -4,8, : Dc1 = ir: 10'+ r, + 1o2 + t':10,5' + 13,5'; :92,5t a', : 2OO + 2f : 110,25 + 1A2,25l' 20O + 2x', : 292,5i 2f B LABB\ BB1': AB'z AB":15" 46'25',:225 46'25:178,75 B LBB? BD2 : BD2 + BBt2 : LO,52 +11a,75'z - 110,25 + 17a,75 : BD: J28s =17 (cra\. 3 L DCq CCl' : BB1'z :174'75. AC': ACI', + CCtz : 13,6'1 + t7a,75 : 182, 25 + 17a,75 = 361;

idb:

CC\ Ha

Biano

ABCM CM = CBsiD ZB = a

e d.

ocxinbRn Bc IAD i AD € a, ro Bc ll q. D BB, c01fl( aBa repneEAt(yrspn ao oalliei fl,'IoqvElr. flnorJl{rra, sKa rpor(oAlrrb .]epea npaBvnbHi npnMi Bh i CCp reperrEae nnoqlIrry (t ro npsMii .B,C,, B\q I BC 'loni BPCCr rpnMonvrlrn}i, B,C, : 10 cu. 3a o3EaEoIo rapatenbHocri rpsMEx B,c, | -4r, 3a aoBeaeEIrM BlCj : : AD. Toai. ABPP rapanenorpaM. 3a B,'IacrrBicrm naparerorpaMa cyMa rcBaApariB rioro cropiH AopiBIrIo€ cl'Mi RBa'4-

1., TapaceHKoBa H. A- :ii::i:i:::::.x::i::ii:iii::::.'i::

2.8.

Ne2 1.

2,8.

3, B. 4. BiAnMiAb: 5 ct"5.

5. B.

[::il::iiii::til::ii{llill:i rEoMErPle sypAa M. 1., rapaceRKoBa H.a.

i!:i

843

OcEinr,Rra 6icercrpsca &yra piBlrocropoHEEono TpnKyrsrxia € ioro r,{eAiasorc, ro Ba{aqa sBoAurbcs

NOBTOPEHHC CepeAr.tlnr rp6ox pe6ep tipaMiAn qe rpr'I rorrnr. 3a EacniAKoM 3 aftcioM crepeoMerpii qepes 6yAE-sni rps roqltlr, ulo Ee nexarr' Ha oAHifi npflMifi' r"to)+(lra trpo_ Becra trrorllssy i Ao roro x rinbnlr oaBy.

542.

Aaxa dpaMiAa' A1, Bl C' - cepeAnxu pe6ep S,4, SB nroultIHa -41BrCr napatenEEa nnot{! d ocEoBr, 60 rlpoxoAr.rrb rrepes rpsMi,4lBr i B,Cr rnoqrsn -4,-8,Cr, rapsner6Ei trpsMrrM.4,B i BC trtoqssn.4JC (sR cepeAHi nirdl

543. SA.BCD

rpuLyrEnrca).

1) Toni-4rr! 11,4, i

oa reopeMolo oaneca

SD. BiAnosiAb: tata. 2t lli, 6o {BP I ll ABc

cepearEa

,qo Bl,ltra,qliy

554.

Bk)nosidb:

Mor{lHa rpoBecrs qorr-rpE

qe pe6po nv6a a, Apyra

o rapanenEEa rnoqEEi p, ,.F € 0, roAi o llDF, eo uaxEe trpsMe a i rlnoqEEa P Manu 6 crinEEi ro.rrir. AjranoriqEo, ocninrrlt' b I d, ro b I DF. Toai sa o3HaKoIo napare,rseocri npsvux a lb.

556, IIpsMa

itii:.]!!

Aiarosatr, ioro

s pe6polt

,",i

tO iOC:1t2,

oc =?Ec = o-E .?

tftqo =

"'8

a6o

rnoqr.rEi p, Mofie 6yrll Dapa-

fleperrnarq n,roqzsy

P trapane ,Bi, ro rpsMi a i , Mo$ryrr,6yrlt a6o MlrMo6isHr.rMu, a6o DapanenbHtrMx. gKlr{o IInoqIIIrIr o i p DepernHarorr'cs, ro nptrMi d i D Mor{yrb 6yrlr a6o MnMo6i,rrsnMn, e6o flapanerEE[Mr{, a6o fiepernsatllce,

s*'"=|zc no=!

Eerc

cnin|l{ x

rotloR.

Mo}tcyr6 6yrr.I MrMo6ir{iErMn a6o [apanerEHr'IMtt.

r{oaEoi;

napa"'renhHa AaEiii

2) 6$ri'r;

tnoultHi. 3) oAEy.

flpoeHqiero ABox npEMt{x, srii treperrEarorl'cs, MotKyrE 6yrl trpsMi, rqo neper[sarorEcs, a6o trpsMa (s&qo [poeRryBatbHa fipfiMe naps{et6sa tr'roqfiIri rlt x

564. 1)

rpsMInx),

2) Ilpoe&qi€r [apanerbErrx trpsMl{x Moi{yrL 6yra: a) aBi napaner6si trpaMi; 6) oaEa rpnMa, sKrrlo trnorqr.rEa aaHnx npsMlrx napatenEEa rrpoeKryBanbsiii rlpsMifi; B) ABi Toql{n, sKlr{o npoeKTyBarIEEa trpsMa trapanetr,rra Aalrt-rM. 3) Ilpoeriqien MzMo6ir{Hr.rx rlpsMltx Mor{yrE 6yrn: a) npfiMi, aKi leperllEarcrr,cn;

+ +=++=+

6) trapanerr,Bi npfiMi, sHlqo trpoenryBanr,sa [paMa napanetbEa nnoq]IrraM, fierrcars rq[Mo6ixHi rpsMi;

a'-.!E a,!E

:-=vz:!r.

rEoMErPle 6ypaa M.

56O. npsnaa trapanenbEa n,'IousEi, 60 Ir€ Ma.3

563.

ro'r&a rleper]'rl]y

Do = .t6c" - oc" =

844 f;l

562. Hi, rinhfir rxrqo EprMa

9€'

B LDOCI

s.""^ ..4=

MrIMo6i1.rEnMn.

561. ,qani rpsMi

EyFaF,rii nepepis.

Bcsineo'=

3a Bnacr{Bicrlo MeAiarill, MeAiaIr,

6yrn

559. fl&qo trnoqrEr (l i

lt t:..

^BEC

prMi b i c Mor+ryrr,6yrx napa,,ren!,sl{Mr{. fleperrlrarfics

a6o

nenblla

DC: a' s

557.

or.

.558. IIpnMa a Molie re,Iiarl,

:1.!l+i:'

:*:::l:$

ro.rox,roalan.

rani

=.,tE

548. 1\ DABC - Aatla nipaMisa. CE MeriaHa ocHoB . ADEC !

osEal{orc).

2) gfiLqo npsMa a traparorrsa n"roqrsi F, ro BoHr.r He MabrE cqin Ocxinr,&$ o6aaBi npsMi a i DF nerrcarb B oAHii trroqr-rEi d i He Malorb cninr.Etrx

tre

Ilroqa rpani nipaMiar :

(sa

cDiJTEsy roqRy. ro BoHu nepernsalotEcs tro Dpf,Mifi.

rpani - a'12. rori rrroqa trepepisy S, o'uE. flnoqa rpaBi S

. a"A

oupaneraao a, roAi

rqo npoxoanrE .repes qro rocxy.

cropoEa raKoro trpsMoKyrsnxa

Sa'l

ABoM AasxM

555. Hexafi rnorqlrErr d i I reperrrlarcrbcs ro rpn' Mii ,-8. 3a axcioMoro 3, sftuto ABi trJlorqrsr MarorL'

547. y xy6i qorllpl, trapr rportrnen(Ilrx pe6ep, roMy piBEi rpaMoKyrnlrkrr. trepepi3r.r. yci iroIIr.I

s,.

op"ny

IlpfiMl'Maib

rqlHi.

OAsa

Hexai roq&a-4 lre sane}I{rrr, i 6. IIpoBeAeMo

.repeB ro.rfiy b. ByAl,-sxa trnoqrEa, qo" rpoxoarlrb rrepe3 npfiMy c, trapanetblra

,sC.

rp,l roqxu. qepe3 asi ro'{l(l'r Mo}xEa npoBecrn 6e3ni'r nnoqtut. roMy seraMKHeHi ABepi pyxarorr,c.E, ro6rc npv fiMarorl' 66ni.r rono}I{eEl'. Tpr ro'rllr'r BEsga.{alorb oAEy rrnoqnny, roMy 3aMEEesi ABepi OiKcoBaFi e Iliii trnoi 3aMoH

MeAiaHa.

trapa-'renBsr.rM npsMqM a

3) Hi.

544. Asj trerni

Ee3ni.r,

1): D-E

B fiIcl,rx

B) Toqlla i np€Ma, s&rqo trpo€r{TyBarl'Ee npsMa [apanenEEa oaEi]ii i3 Asssx flpfiMnx. 1.,

rapacexKoBa H' A.

ililiiitlilltllltl:.:''$;lj

F:tlJiiltli;lL!;iili:t::j

rEoMErPle 6ypaa M. 1., rapaceHKoBa

H. A.

i:;ii

84s

565. 1)

SICIIIo BiapiqoK

2) flKU.ro BiapiJoR 3) HiKon'.

566-568. npz

napanerLlrlri rnorqttHi flpoeRqiii.

He napanen6Hrii Ej]otlrnHi npocKqii.

napa"renbrroMy rrpoeriryBaHEi s6epiraerEcs:

1) rapanerltricrb ocHoB, cropiE; 2) rporopqiiinicrb a6o piBEicr6 BiApi3riiB oAHi€i npaMoi a6o napanenbrr'l trpsMr'Ix

BiApi3na B cepeAlrHv tiapi3Ra' ce IlonoBlrsi croponr roqo). He B6epiramrr,cEi Be,'ItI.rrHIr xyriB, nepflesAfEynspEicrb, piBsicrE a6o rponopqifi }]lcrl) BrApr3KrB, sKa nep€TlrHaloTr,cfi , (MeaiaEa rpoelrry€rr,cs B MeAiaHy, cepeAzHa

peAII.a

riHin rpr&yrHrrca

AopiBHroe

569. Hexaii 4.43C npoellqi.n

AaHoro

LyrsltKa.

ci.rHa Dnonrmra napa-'1ej1r,ra ocHoBi ripaMins, ro repepfu (BaApar. npsMoxyrn{n i rapatenorpaM y nepepisi orpl{Marlr Ire MoxHa, sR i lrrecr{&yrEnH (He icHy€ nnoulqsr, .tRa neperllHa€ ricrE pe6ep ripaMia{).

572, gKuro

. B 60', roai - A 30". BC 2^ .4-8. EiccKtprca BD ri,1 rb cropoHydC Fa Biapi3rcr, tporopqi;si BianoBi,qErM cropoEar: AD I DC: AB I BC :2 | l. }lexan BM 6icexrplrca 3oB-

HEoro rivra

rDr

BeprJd

'JiB.Toni.ZMBK:ZCBN:60'. LABC: LKBC 3a nareroM i ro: AC.

crpr.rM r(yroM, roMy CK

OcriinBnr rpl-I napatenbHoMy trpo eI{rr.BaEEi i3 posrn.EHy

Bocreii optr sa,!a 36epira€rr,cn rrtrle nponopqiiiEicr6 Braprsr[B oaErel np.aMor, [naH flooyaoBlr raktE: ( t. Harpec.,ruru aoBi.rEtrt'i rprKyrHnR,43C. 2. [o6yAyBarr npoeliqilo 6iceirprcr B, ra:f', D\o AD I DC : 2 : 1. 3. Ha rpoAoB)rceHsi c'opo:dtt AC BlattlafTr{ CK : AC. rlpoenqirc 6icelcrpncll soBHirrEBoro Ryra IIpI, BeprIIrIIi B. 4. fio6yAysarr B-K

570.

op'risa-!a. -4-BC, - ItBaApal. aep.a"'4a Ba. OM vcriaHa I Bucora piBrro6erpeHoro r peMoHyruolo rpxr{) rHrR€. Toa:t MMO piBEo6eApeld. flpoBeaeMo MN LBD i ACMO - rpnMonyrEi i MN L-4C. Toai N i tr BiAnoBiAHo cepea H' BiApi3IdB BO i CO. IIpr napanenbEoMy trpoeKryBaHEi 36epiraerEc.s raparer6Hicrb cropiH KBaApara. piBHicrb ra npoqopuifiHicrb Bi,qpi3RiB onnie-i trpsMoi ra rapa-le,1bH]rx npsMlrx.

-..

, ".):*tt-...

Po3rn€EeMo BnacrllBocri

[o6yaoBa. 1. fiaparenorpaM ,A'B,C,rr ABCD.

846

P: I

= CBr = '16' +

cl o1

(cM);

: 28 | 2 = 14 (cM); = {4.6 d = 8vEi cM').

B0)' =

+ s2a

DB, =

ure - n"

W 3)

li:{li.lii;:Jil::iiiltlitl

o". =L2244

".o

=\600

so ("*); A

\/4

D tAC. D -

cepea'\Ea

t "Ji

!l;!!:{ .L]t-1t -1Lii:{

AC.

ActDc=tb-ia. =

rt,

'uJn.

b:3 i 2, aoai a:1,5b. 4) de, =ca, = uE *t' = tE,rbb\ b" =,lr,rib" = au6,zs nn, = rtr,c" - nc" = - o,zst' = oJa. "E,zrr' p = b + 2b\E = b(l + 2\b). s = f, r,. ne =b!11. 3a yMoBorc

ff , E i*, r t "f 4r" =

'l!:.:.t

!5.1s€ rd =2?!51 (cM').

+ r'" =

npoBeAeMo Bucory B,

piBHo6enpesu;.p'ryruyx

+,10 + 10 = 28 (cM);p

i::i: TEOMETPI9 EypAa M. 1., TapaceHKoBa H. A.

= 10

=CB,=J""+b".

1) ABt

3, AB,=CB1='1""

rpaMoi,4C.

€m

3 A.4A,B,: AB,

s=uE9(i9-18Xs9

81O,, Ii, 2. N, - cepearEa O1Cr. - cepear.Ea rpoeKqis neptrenAr.IKynnpa 3 ro.r&r M Ao 3. M1N, trpoellqi.f neprenArl{ynnpa 3 roql(r BD, M8,

2\ AB, = cBt = J24" + ra' ='6zo P=18+2 30:78(cM); -p-7a.2:39(cu)t

npoeRqia kBa,qpara

CB,. nepepi3 A-B C

Brkrr. ro!i A-8,

s = !/i7G4 - 8X14 10)'

AC L BD. M

:."ir--

573. OcKinbKn npt att ABCAP'q rpaBrr,lLEa! ro ii 6iqHi rpaHi - piBlIi npaMonvr-

!i:!:i:iii:ii:::i!:iiiiini:ii:r |-EOMETPI9 EypAa M.

o,so'G.

1., TapaceHKoBa H.

ii:l

847

574.ABCD EpsMoliyrglr(' O feperr-rEy ararcE'a.neia, MO L ABC, - ro-{&a AB: CD - a, AB : b. ZMCO : o.-. s Ac '1,"n' t co' = 't"' - o" . ^ACDt

oa=!ac='la 22

lOJa

2.3 r,6 cM. ---

- zo-€ = roJI

-4C :

8 cM' Be

€rrrercbni).

fpr

(cM).

MD = Mo : sin45" = 4,

12 cM.

-L

BC aa reop€Molo

neprerrar.rxynspn.

a,[z C*t,

=* =* f2135 ot; "i" cru. 8idao6idb. 8 cyi lJz "r.al

5AO.

A/-BC

FB = JBc\ Fe =.h2" t5" = Jt+++m Bianosidb: 5 cNt, 5 cM, 13 cM.

- "Ees =fi

ro.rEolo tr.p"t""y t; AinsrEcs EaBrin, orr{e, EpoeRqii Bcix roxlrnlrx Ee piBHi. 2) Tax. fir qo rpatreqis piBEo6i-rlra, ro AO : OB, ,O: OC i BiAtroBiano AF = BF, DF - CF. gnuto rpaFeqis trpaMoriyrHa, IrarpnKnaA,

B LAOBI AO'

" A(, = la'-

576. l) Hi,60AiaroEani rpenelrii

ZA: ZD : 90',

to AO

DO,

,roa:.

DF.

Hexafi AB i CD - BinpirKx. O - ro'rRa rx nepernHy. .4O : OB, roni AM - MB, y piBEo-

577.

rpxxyrHrj(y AMB MO i Bdcora; MO ,L .4'8.

MeaiaHa.

i Brcora piBno6eAAFanod':Eo, MO - MeAialra peBorc LCMD. TaKur{ qvBoM, MO L AB i. MO I CD, ro(i. MO L a sa orHaRoro trepneHAlafiynapnocri DptMor

i finotqrrHtr.

ii Epoel(uis. - noxrna, OE 3a yMolorc OB : b. Ilexai! AO : t, ro4i AB = 3a reopeMoro Ilitbaropa AB' : AO' + OB'z. (t + a), - x, + brt r, + 2ax + a, : f + bri

578. AO I d, AB

r + a.

a'-a' ^ '2a

848 llii rEoMErpre

: BC; 2BO' : : AB' BO';

Eyp,qa M. 1., rapaceHKoBa H. A. i:illll{li;:i:llit:.i:ili:l:.ii.

la' a 1-=:==

2 = '{2 J2

BidnosiAb: 1)

581.

,"^,,

piBno6eApeErn tu EyroM 60" trpx BepEraHi, roAi A.4JC AC = a.

Eii4, BC = AB

g LBOC: BO' + OC'

MCB,

6eApeEoMy a sEa.r}Irr,,

'12

AO : CO : 4 cl,r, fa sx troxuni, rqo MalorE piB: IC : 5 cM (M,FO i AC-FO BC, roAi FC

12'5 (cM)'

l = a tcMl:

579. MA = MO: sin30'= 4:

(cM);

cepeAnEa ,4C, roar

3a yMoEoro -4C B

rEb6 + 144 .tE

?'5 +

treprreEA[fivn.Fp sin I

Mc - Mo,sin6o. = 4,

FO - AC, Af : Ei npoeftqii, .41

apo

ro'5

cr'r; 2)

575. Y LABC zC : 90", O

='oori'u =7'5 (c'ii AB:

" '=tou.ru' BiAno6i0b: 1\ 17 ctni 2') 12,5 crtr-

.tec-

ro-@:\@

BiAnosilb:

.4.B:15+2:1?(cM)i

*o={t:E-E-

=rs t *\,

= Jo\ o"2-,

lutu = uc tgcl

,=t !=6a;a

^t;

T;z

a'i no" =

pisHocropoH-

t. 2

a\12

2l o.

: u. - poM6 si. c'lopoEoro a, ZA roql{a repernEy AiaroEanen, O-F : ,,

-4-BCD

OP I ABC. IlpoBeAer,ro .F'tr

t CD, ro4i OK L C, sa reopeMorc flpo rps rrepneFgarcyjrsptr. 01< paniyc xona, BrIIIcasoro B poM6. I OK =:.LK- icLK Ftrcor6 ooM6a. 2

: a' sin C[.

irl

oro 6okv

S,: CD LK: LK =

s" CD

, , 1--LK=-a'?sinc asinc U1<LK= asind , 2222 z

^FoK

FK=

FK =

a s:'n" ct 6F' ' oK' .lu" \4 -

1'.^

i16+fr

i*i:ltltlti:l{ltJii:.:t:i rEoMErPle

=J16+s =5

{cM,;

Eypaa M. 1., rapaceHKoEa

H.r. il:l: ang

I I

i " 16" sin'60' zt !^=14-+

2|.6..

riro* l4

a =,4e+ns=Jon=s

r"'t.

542. Hexan MJC - piBHocropoHHifi, P,,F.: P. MO . ABC - BiArraFb si.q roqKa M Ao n,lotr{xH}r rpniyrHnfta.

Ocki,r6ftrr ro.rKa l,t piBHoBinAanpHa Bi4 cropiH rpnI{yrqerrrp ftora, BrncaEoro B A.4BC, O xr.rxa, ro O roqna repernHy Brrcor i MeAiaE. IIpoBe.4eMo,4, I BC, roAi MD -L BC aa reopeMor npo rpn reprreHAr.rKynsp*r. MO Int'Kana BiAcraHb.

MD:b.

-t; itE -66- rs

61,402

t[6

= JMD"

1) MO=

'/ieg

ln'6J' (

2' MO=

"/i66 i;; C;

=,1 =_

(.ont;

(cMr.

IIpoBeAeMo .repe3 npnMy c

I c aa oalIalloro napaJienbEocri npsMr.rx.

llno f! {y p,

eptreEAtrxy

cr.

y. nepneHrxky,rrpuy nprvii d reperrEy nnorqrq o i B. BoEa neperse nnoqlrrls o. i B ro npnMnx CD I d. j. BD I d. CD L d, Bat'\!o3,o!

i.ii!r:.:.:.

c]M,

17 c].,, AB

28 cM.

SMCD AD=lAF -cd =.tn" -t{

AD + AB

3 tBcD

: I + 28 :

=.lt-o' -

36 (cM).

eD: = Vis * 3d

* tzgo = Jtrzr = = '6zs 39 cM. BiAno6iAb:

as ("*1.

544. noxzna- o yrBopro€ si croposaMr rrpsMo.o Ryra BC, piBHi Rlrn: -AaB - -AaD - 60". Tori ocnoBa treprFHAlr(yr.rpa .4O Ao r,'Ioqrllr.r kyra rer$rrE sa iioro 6icex

rprci.

IJpoBe4eMo

AB L BC IAD LCD,'to4i OB L BC \ OD LCD

Jd upo rptr uepreHAxhy.rrpr{. BODA - ll-BaApn'euppMUU (BoDc 60 oD I Bc i oB I CD, - 'apanenorpaM, BC : CD, \e }xIJn Bae 3 piBHocri A,4l9C i MrC aa riroreHForo i rocrpxM ftyroM, ZC : 90' Ba yMoBoro).

8so

r:i:::

"n.'

rEoMETPtq Eyp.qa M. t., TapaceHKoBa H. A- :iii!:i!;l:i:!:i!:ii!j;!iiiiifi

.1""

.-t*A\

o,.

s.,

A e a. BC

a, AC

BiAcraEr, BiA seprur-

- rrpoe(qia rinore1lysv'la ton\u]{y s..1ABA1IllyllaEnii. AC L BC,'toAi AP I BC aa reopeMoro trpo rpL, rep -4rB

neHAnrlynspu.

t BC'=

l'ABc AB = nEe AA

"lt

. r' .

/aBA =t=_. AB Ja' + a' t,,rcn.:2o". l0 sin .4BA 4 -=-AJI44 -256-\o 20 2 AB Jtz' , t6sin

=r/zss-2%=J6a=s("llt. BD

1l\\r/

10 1:: o 60'; Jo'+e' 'll coso ' 2.10 2.10 2 * 1d -:-:: Jtoo 1 '-:--:-=2t cosg- "/11 - V-45o. 2.10J2 = 20.12= .12 Bidnosidb: lt 60"i 2t 45'. stl A ao firloi\u'ltt

ITpoBeAevo nnoqusy 1dr-..:.i!:!ii

/FAO = . FBO ZFCO E{rA Mr}{ noxhrxvx A i rl,'IoquEoro rprr(yrnrrKa. 3 LABe AB-.lAC'-Bl = jo 4.

t',

30",

,eHa Bia BepIIIrrE 4,4-BC, ro roqxa O qenrp Eona, oflncaHoro EaBrco,'lo A-ABC. O rinoreHFE .4.B. - cepeAliHa LFAO MBO AfrO Ja KareroM i rinoleHy3oro.

2' ,aAao:45..

585. AABC npsMollyrErn, -4C : o, BC : A. IlpoBe,qeMo IO L4-BC. Ocfti,'rb(z ro.rKa -E piBEoBi,qAa-

IIpoBeAeMg.4-4, L cr, .4-4,

sa3. ocrinbns c Ia i a lt, ro al

AiaroEanE RBaApara.y LABC ZBAC

'rE

586. AABC rp.rMoRyrsrrfi, BC e

BiAnosiAb: LJ '1166

nspEy trnoqEEi

a.l2 sl{

arE

BiAnBi'b:45".

ao = L as - Ju' 22AF

OD" =

3 LABCi coslACO

BiAnosiAb: 1) 5 cM; 2) 8 cM.

"" -' - iTs-

IIo3Ea.rqMo BC : a. ToaiOC: 'rovty AC : 2BC = 2a.

nnoqnEa o repnenAllriyj1Fpl{i Ao npsMoi r. Oc(inbElt rpsro.rep$ rpsMy o MoJnEa trpoBecrlr nnorquay p, nepnenanKyrspsy np.sMiii ,. IlnonlnHu o i ll napanenbHi, 60 BoI11r o6uABi neprelrArllyn.tpsi npsMiii b. SEaqrrb, rpsMa a, s&a JretnlrrE y r,roqzHi p, He Mae 3 rnoqlrnoro o cnirltrux rovox, ro6ro a la.

5a7. Hexan i

Mi a

trpsMa a

b reptreEAnKyn.npHi,

588. 1) AABC

trpnMoriyrHr.rn,

-ZA:90',

20 cr{, AC : 15 cNt. Hexak AAt I o. AA- uykaHa Bi4crasL Bin Beptn{Hv

-4 Ao

trnoqrEr

C[.

lpoBeAeMo AK -t BC,

rpr

roai,41r I BC

3a reopeMolo

rpo

reptreEArrr{yrnpr.

;titl{iitlitii{a:.1:;::i rEOMETPlc sypaa M.

1., TapaceHKbBa H.

irl:

8s1

ZAKA\ =

ftyr

flrolqssolo

Mfuir

i d.

AA-BC

B LAJ,C BC =.tEE + AC =.1@ +t5" = J4oo 1225 = J625 - 25

(cN^t.

Aa' : BA KA;KA:Aa':lla: "" -" "-XC=!42 25'

AK=JAC'-Kc" =rEE" -s" =.t22s-sr=Jlaa=n

@Ni.

-=6 (rM\.

- Afsin3o"=12

Bidno6idb: 7

(cM1.

nc ..ax,

^AJ<A

AtsCD

IIpoBeAeMo

60" nJa f2

.4r( sin

poM6,

BB'

592. ljexai, y LABC 1A =

gO",

IIpoBoAnMo BBt L &

CCl

A e d, BC a.

l d.

AA,B,Cr

BB, I CC, ak ABa EeptreRnrjxynnpx no onHiei rnorqrgrl; ocrinbxll ,aC ll ct, ro Bh = CCr foai BTBCC1 rpsMoftyrH'(, BC - B1Cr.

(cMt.

3 A.43rC, 3a reopeMoro &ocruyciB

1c',r1.

,4, € d,

Bpt'z: BC

IuiCClIa,

cx,

cM.

trpoeKqia aiaroEani dC, DB, : 3 - rpoe&qis aiarona"5i DB, BBICIC "*npaMoKlan|.K, BC BtCt.

3 MCCr:

-'rL

='6

= z.]s kM).

3 DBBI:

=1EE

BD =.,8r;", + 4D" = "ire AiaroEani poM6a repreHAr.r&yrsplIi.

+ol

s76-2 A.24. 2 =657. 'foaj. BC'-- BP" : 657 no3Ea.IrMo.4.B = !, AC : A. 3 MBc x' - y'z ' 6574I) D' -DB'. 3 LABB\ AB': AB1' + BB12 ' aBiAk'J BB.' : AB1' - AB'zt BB1' : :t' - g. 3 LACq AC': AC\' + CC1'z,,eFj.a:!':d CC\' : AC' - ACt'i CCt'z= y' 576. Oc&in6&tr BB, : CC,, Ma€Mo cncreMy piBnsHb:

AC1: 2 c$t

Ac =,[Ac: * cc: -'12" + 4"

3'z

B,C,':9

BC I a.

B4:CCr:4

+ ACt' - 2ABl Aq cosl20" + 24' + 2 3' 24 cos60'

Bpt'z: ABt'

BiAnosiab: 1) 6 c!6t 2) 6 ci{,

589-

c!,t.

oproroHiu1lHa rpoeEqir rplr&yrl{rfta -43c Ea

25. 2.20J3 4lr = f= =4JJ Ba 10 3

CHopucT aeMocb pe3ynbraroM nonepenHLoi sanaqi.

CCj: BBl + DD; DDt: AAt + CC1 BB : Dq=17-12-22-7(cMr.

=.[5-5-2 8=

2oJs

BB + DD, oo,'2 --t :.':) flH .epeAHt ,Ijsi'] rpaneqii B,BrDr. AA-. ''CC. BB. DD. --r . -:--, BBt + DDr sBialttl AA. t cc SHaqnrb. j:a 22 AA1 +

MJc, p-10*13*7=15' 2

s"=0b(1b 1ox1d 1 = \8.5.b 2 2.4 =5 4J5

niHin.

591.

2) O6ipynryBaEHr MsrroElca allanoriqEe Ao 1). 3'afiaeMo nnoqy

OOt ii cepeaEs

Ananori,rHo.

KC=225.25=9(cM). 3 LAKAT 4

A,ACq - rpane\i.a, 4,4 + CC. (t(l=L

'60

=a.,/B t"*1.

oc 1 ec Js tc't. 3 LC?D cD, = oDz t oC.; co ,lzoE t rcv,, s Dc,=.FA -cc: =.15" 4 =.85-t6=Js=s

fx" +y" =657, l*" -s= !t" sta;

oD = BD - 2J5 (c*.)i 22

^Dcc,

!x'+s'=atz,

(cu).

BiAnoqiAb: 6

BiAnoaiAb:3cvti5cMt.

590. Hexat .4rCD

trapanenorpaM.

IIpoBeAeMo.4Al, BB! CC! Drr trepreEArrriynspEo Ao nnoqrBx cr. Ilapa,renorpaM ATBTCLDT trpoeftuis 4a

rfioqasy d, 3'pAEarMo BiApirxoM roaa[O iO treperaHy AiaroHanefi naxoro trapaienorpaMa i fioro npoeKrii. AA, I BB,lCC, DDr rK nepnes,erKynsptr ao oaHici EOrO trepanenorpaMa Ha

trnoqr.rErr.

852 iltj rEoMETPts

lx'-c'=-tzs: : 9O:. x' = 45. 3 MBB. BBt': 45 2x'

Eypaa M. t., TapaceHKoBa H. A. t ltl::l:il:f::ttti:::iJii{

I, BB\':36;

BB1

cM.

clI.

593. S

MEoroliyrHtKa,

- nnoqa Sr:Scosq;

51 [noqa

npoe$qii,

I - Kyr M Ic trrorqtnaMn.

'"s

56 '1122

q = 60".

ilttii:il:::itli-:*iiti:.i:i.tt rEoMErPlt sypAa M.

1.,

rapaceHKoBa H. A.

{r1j

853

594.,'. .5

lr)r ..siii)

tn^,.,:

' l

;I (l]:

IOtj ,

ll .

,, ,,',

l:,,,,

ltrttt,,tia\: 1J; 1 , rr': l)

i: i,::.:-:

.:.:.iii1:.: . .:.:

il:.i:.

-it::.1:

n00 ,. r

r;rro

r'.