Lesson 11-3 Inscribed Angles

1. Lesson 11-3 Inscribed Angles

2. A B C Definitions An angle is an inscribed angle if its vertex is on a circle and its sides are chords of the circle. For the circle above:

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

4. Find the values of the variables.

5. A D B C Corollaries to the Inscribed Angle Theorem 1. Two inscribed angles that intercept the same arc are congruent.

6. A C B A C B A C B Corollaries to the Inscribed Angle Theorem 2. An angle inscribed in a semicircle is a right angle.

7. D C A B Corollaries to the Inscribed Angle Theorem 3. The opposite angles of a quadrilateral inscribed in a circle are supplementary.

8. Find the values of the variables.

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

10. Find the values of the variables.

11. . m A = 100; m B = 75; m C = 80; m D = 105 m X = 80; m Y = 70; m Z = 90; m W = 120 . No; the diagonal would be a diameter of O and the inscribed angle would be a right angle, which was not found in Exercise 1 above. GEOMETRY LESSON 11-3 In the diagram below, O circumscribes quadrilateral ABCD and is inscribed in quadrilateral XYZW. 1. Find the measure of each inscribed angle. 2. Find m DCZ. 3. Are XAB and XBA congruent? Explain. 4. Find the angle measures in quadrilateral XYZW. 45 Yes; each is formed by a tangent and a chord, and they intercept the same arc. 5. Does a diagonal of quadrilateral ABCD intersect the center of the circle? Explain how you can tell.

12. Homework: p. 601 1 - 24