1. 11-3 Inscribed Angles Objective: To find the measure of an inscribed angle.

2. Central Angle (of a circle) Central Angle (of a circle) NOT A Central Angle (of a circle) Central Angle An angle whose vertex lies on the center of the circle. Definition:

3. Central Angle Theorem The measure of a center angle is equal to the measure of the intercepted arc. Y Z O 110  Intercepted Arc Center Angle Example: Give is the diameter, find the value of x and y and z in the figure.

4. Vocabulary Inscribed Angle Intercepted Arc B A C

5. Theorem 11-9 (Inscribed Angle Theorem) The measure of an inscribed angle is half the measure of its intercepted arc. B C A

6. Example 1: Using the Inscribed Angle Theorem P Q R S T bobo aoao 30 o 60 o 60 o

7. Example 2: Find the value of x and y in the figure. y  40  x  50  A B C D E

8. Corollaries to the Inscribed Angle Theorem 1. Two inscribed angles that intercept the same arc are congruent. 2. An angle inscribed in a semicircle is a right angle. 3. The opposite angles of a quadrilateral inscribed in a circle are supplementary.

9. An angle inscribed in a semicircle is a right angle. R P 180  S 90 

10. Example 3: Using Corollaries to Find Angle Theorem 60 o 80 o 1 2 3 4 Find the diagram at the right, find the measure of each numbered angle. 120 o 100 o

11. Example 4: Find the value of x and y. 85 + x = 180 x = 95 80 + y = 180 y = 100 xoxo yoyo 80 o 85 o

12. Theorem 11-10 The measure of an angle formed by a tangent and a chord is half the measure of the intercepted arc. B C D B D C

13. Example 5: Using Theorem 11-10 35 o yoyo xoxo Q L K J Find x and y. 90 o

14. Assignment Page 601 #1-23