1. Section 9-5 Inscribed Angles

2. Inscribed angles An angle whose vertex is on a circle and whose sides contain chords of the circle. A B C D are inscribed angles.

3. Theorem 9-7 The measure of an inscribed angle is equal to half the measure of its intercepted arc.

4. A R T Example: If m = 45, then = If then m = 54

5. Corollary 1 If two inscribed angles intercept the same arc, then the angles are congruent. 2 1

6. Corollary 2 An angle inscribed in a semicircle is a right angle. Circle S S

7. Corollary 3 If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary. Q A U D are supplementary are supplementary

8. Theorem 9-8 The measure of an angle formed by a chord and a tangent is equal to half the measure of the intercepted arc.

9. Example: T P is tangent to Circle O A is a chord in Circle O O If m = 140, then =