Zadaci okruzno 2007

Page 1

! " # $ % & '()*+)'**,) +) " D

F

E

C G A

B

! ! " # ! $ % 16 m & ' ( ) * + ) 176 m2 ,( % * + ) ! Æ ( $ ' ( Æ 16 m ) ) ! Æ ( $

) x ( x

x x

- . ) ! /0/ 1 ( ! ! 1 ( "

! ! /

! 22 1 ( ! !

) / 3 . + 4& 56 = 758 5 , ( 1 ( ( 1 ! 9 ( 4 ! ( : 1 / 3 ' ! ( %

- . . '* . ) - . - . (/* )

0 1 - . - 2 ) " 0 3 4 )


! " # $ % & '()*+)'**,) -) " a b 1 a 3 2 < 10 < 4

a 10

+

b 15

=

5 6

10 m 1 dm Æ

1 m 5 km! " p# q r 2p + 3q + 4r = 2006. $ % & '( $" n # & " n + 1 " n ) * + ( "

. / / '* / ) . / . / (-* )

0 1 . / . 2 ) " 0 3 4 )


! " # $ % & '()*+)'**,) -) "

a b a+b = 30 198 a 2005 2007 = 223 + b ABCD AB > BC

p

O BD AB M CD N

M BN D

a b ! a > b" (a + b) · (a − b) #

$ % & ABC D E &

AC BC

ADE BED AB " AB = AC+BC 2 '

( ) cm*" 2005 cm

. / / '* / ) . / . / (0* )

1 2 . / . 3 ) " 1 4 5 )


! " # $ % & '()*+)'**,) ,) "

√ √ √ 17 + 37 + 2 > 3 5 +

10 cm

32007 − 23000 2007 · 22007 1 cm 2 cm 3 cm !

" # $ " % #

$ #

& '

- . . '* . ) - . - . (/* )

0 1 - . - 2 ) " 0 3 4 )


! " # $ % & '()*+)'**,) -) " 20072005 − 2007

30â—¦ 8 cm ! "

# ! 12 + 22 + 32 + · · · + 20052 1 · 3 + 2 · 4 + 3 · 5 + · · · + 2004 · 2006 $ % BC AD ABC ABD

E & AC

6 cm' BD

3 cm' ( E AB ) * + , , +

{1, 2, 3, 4, 5} !

. / / '* / ) . / . / (0* )

1 2 . / . 3 ) " 1 4 5 )


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