Chapter  10  Cheat  Sheet  Â
Tangent  Theorem  (Lesson  10.1)  In  a  plane,  a  line  is  _______________  to  a  circle  if  and  P  only  if  the  line  is  perpendicular  to  a  radius  of  the  circle  at  its  _____________  on  the  circle.  Tangent  Segments  Theorem  (Lesson  10.1)  Tangent  segments  from  a  common  external  point  are  _______________.    Measuring  Arcs  (Lesson  10.2)  The  measure  of  a  minor  arc  is  the  measure  of  its  _____________  angle.  The  expression  đ?‘šđ??´đ??ľ  is  read  as  “the  measure  of  arc  AB.â€?  The  measure  of  a  major  arc  is  the  _____________  between  360°  and  the  measure  of  the  related  minor  arc.   Arc  Addition  Postulate  (Lesson  10.2)  The  measure  of  an  arc  formed  by  two  adjacent  arcs  is  the  _____________  of  the  measures  of  the  two  arcs.   Minor  Arc  Congruency  Theorem  (Lesson  10.3)  In  the  same  circle,  or  in  congruent  circles,  two  _____________  arcs  are  congruent  if  and  only  if  their  _____________  chords  are  congruent.   Perpendicular  Chord  Bisector  Theorem  (Lesson  10.3)  If  one  chord  is  a  perpendicular  bisector  of  another  chord,  then  the  _____________  chord  is  a  _____________.   Perpendicular  Diameter  Theorem  (Lesson  10.3)  If  a  diameter  of  a  circle  is  _____________  to  a  chord,  then  the  diameter  _____________  the  chord  and  its  arc.   Congruency  Chord  Theorem  (Lesson  10.3)  In  the  same  circle,  or  in  congruent  circles,  two  chords  are  _____________  if  and  only  if  they  are  _____________  from  the  center.    Measure  of  an  Inscribed  Angle  Theorem  (Lesson  10.4)  The  measure  of  an  inscribed  angle  is  one  half  the measure  of  its  ___________  arc.   Congruent  Inscribed  Angles  Theorem  (Lesson  10.4)  If  two  inscribed  angles  of  a  circle  intercept  the  same  arc,  then  the  angles  are  congruent. Â
Inscribed Right Triangle Theorem (Lesson 10.4) If a right triangle is _____________ in a circle, then the hypotenuse is a _____________ of the circle. Conversely, if one side of an inscribed triangle is a diameter of the circle, then the triangle is a _____________ triangle and the angle opposite the _____________ is the right angle. Inscribed Quadrilateral Theorem (Lesson 10.4) A quadrilateral can be inscribed in a circle if and only if it’s opposite angles are _____________. Tangent-‐Chord Angle Theorem (Lesson 10.5) If a tangent and a _____________ intersect at a _____________ on a circle, then the measure of each angle formed is _____________ the measure of its intercepted arc. Angles Inside the Circle Theorem (Lesson 10.5) If two chords intersect inside a circle, then the measure of each _____________ is one half the _____________ of the measures of the arcs intercepted by the angle and its _____________ angle. Angles Outside the Circle Theorem (Lesson 10.5) If a tangent and a _____________, two tangents, or two secants intersect outside a circle, then the measure of the angle formed is one half the _____________ of the measures of the intercepted arcs. Segments of Chords Theorem (Lesson 10.6) If two chords intersect in the _____________ of a circle, then the _____________ of the lengths of the segments of one chord is _____________ to the product of the lengths of the segments of the other chord. Segments of Secants Theorem (Lesson 10.6) If two secant segments share the same _____________ outside a circle, then the product of the lengths of one secant segment and its external segment equals the _____________ of the lengths of the other secant segment and its _____________ segment. Segments of Secants and Tangents Theorem (Lesson 10.6) If a secant segment and a tangent segment share an _____________ outside a circle, then the product of the lengths of the secant segment and its external segment equals the _____________ of the length of the tangent segment.