11-3 Inscribed Angles

1. 11-3 Inscribed Angles

2. Central Angle • Definition: A Central Angle is an angle whose vertex is at the center of the circle. Central Angle B K C

3. Major and Minor Arcs • Minor Arc – Short Distance around Circle • Major Arc – Long Distance around Circle B Minor Arc, BC Major Arc, BRC K Use three points to name a major arc C R

4. Arc Measures • Measure of a minor arc = Measure of central angle • Measure of major arc = 360o – Measure of Minor Arc mBC = 100o mBRC = 360o - 100o = 260o B 100° 100° 100° K C R

5. Inscribed Angles • Definition: An Inscribed Angle is an angle whose vertex is ON the circle Inscribed Angle ∠JKL J 100° “Intercepted Arc” JL L K

6. Theorem 6 • Measure of an Inscribed Angle = ½ its intercepted arc m∠JKL = ½(mJL) = ½(30°) = 15° J 30° 100° L K

7. Corollary 1 • Opposite angles of a quadrilateral inscribed in a circle are supplementary

8. Other Corollaries to think about • Corollary 2: Two inscribed angles that intercept the same arc are congruent • Corollary 3: An angle inscribed in a semicircle is a right angle.

9. Theorem 7 • The measure of an angle formed by a tangent line and a chord is half the measure of the intercepted arc. R Chord Intercepted Arc 100° S Angle m∠RTU = ½ mRST U T Tangent Line

10. Example 1 Find the values of a, b, and c

11. Example 2 Find the values of x and y

12. Example 3 Find the values of w and u

13. Example 4Find the values of a, b, c, and d

14. Example 5 Find the value of each variable

15. Example 6Find the value of each variable

16. Example 7Find the value of each variable

17. Classwork • Inscribed Angles WS (pg. 3) in packet. You are to turn in odd on another sheet of paper before you leave class.

18. Homework Assignment 1. Finish Page 3 (EVEN) 2. Study for QUIZ tomorrow