1. Chapter 10 Review California State Standards 4: Prove theorems involving – and ~ 7: Prove/use theorems involving circles. 17: Prove theorems by using coordinate geometry. 21: Prove/solve relationships with circles.

2. Circle Vocabulary Circle Center Radius Diameter Chord Secant Tangent Common Internal Common External Central Angle Arc Minor Major Semicircle Arc measure Circumscribed Circle Inscribed Angle Inscribed Polygon Intercepted Arc Equation of a circle

3. theorems Tangent-Perpendicular Perpendicular-Tangent Congruent Tangents Congruent Arcs & Chords Diameter-Chord Chord-Diameter Congruent Chords Inscribed Angle Measure Congruent Inscribed Angles Inscribed Quadrilateral Inscribed Right Triangle Tangent-Chord Angles Chord-Chord Angles Tangent/Secant Angles Chord Product Secant Product Secant-Tangent Product Arc Addition Postulate

4. B A C D E F G H P 4 4 Find the length of HG 55 o I Find the measure of HI 62 ½ o 9 12 x 8 J 6 Find the length of BJ

5. B A C Find the measure of the arc. 204 o 102 o mBCA

6. Find the value of x. B A C 3 x = ½(4 x + 50) 3xo3xo (4 x + 50) o 3 x = 2 x + 25 x = 25 m ACB = 4 x + 50 = 4(25) + 50= 150

7. examples Find the value of x. B A C x = ½(40 + 120) xoxo 120 o x = 80 D 40 o

8. examples Find the value of x. x = ½(280 – 80) x = 100 S Q P R x 80 o

9. examples Find the value of x and y. xoxo 170 o 30 o 78 o yoyo x = ½(78 + 170) x = 124 y = ½(160) y = 80

10. Given: Prove: proof Q R N K J P Statement Reason