12.3 Inscribed Angles

1. 12.3 Inscribed Angles • An angle whose vertex is on the circle and whose sides are chords of the circle is an inscribed angle. • An arc with endpoints on the sides of an inscribed angle, and its points in the interior of the angle is an intercepted arc.

2. Theorem 12.11 Inscribed Angle Theorem • The measure of an inscribed angle if half the measure of its intercepted arc.

3. Three Cases to Consider

4. Using the Inscribed Angle Theorem • What are the values of a and b?

5. Corollaries to Theorem 12.11: The Inscribed Angle Theorem • Corollary 1 – two inscribed angles that intercept the same arc are congruent. • Corollary 2 – an angle inscribed in a semicircle is a right angle. • Corollary 3 – the opposite angles of a quadrilateral inscribed in a circle are supplementary.

6. Using Corollaries to Find Angle Measures • What is the measure of each numbered angle?

7. Theorem 12.12 • The measure of an angle formed by a tangent and a chord is half the measure of the intercepted arc.

8. Using Arc Measure • In the diagram, line SR is tangent to the circle at Q. If the measure of arc PMQ is 212, what is the measure of angle PQR?

9. More Practice!!!!! • Homework – Textbook p. 784 # 6 – 18 ALL.