Section 10-3

1. Section 10-3 Inscribed Angles

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

3. Intercepted arc • The arc that lies in the interior of an inscribed angle and has endpoints on the angle.

4. Measure of an Inscribed Angle Theorem • If an angle is inscribed in a circle, then its measure is half the measure of its intercepted arc.

5. If m = then = R T If then m = A Example:

6. A Circle S Q S T C • An angle inscribed in a semicircle is a right angle.

7. Theorem 10-9 • If two inscribed angles intercept the same arc, then the angles are congruent. 2 1

8. INSCRIBED • Inside another shape CircumSCRIBED • Outside another shape

9. If all the vertices of a polygon lie on the circle, the polygon is inscribed in the circle and the circle is circumscribed about the polygon.

10. When each side of a polygon is tangent to a circle, the polygon is said to be circumscribed about the circle and the circle is inscribed in the polygon.

11. Theorem 10-10 • If a right triangle is inscribed in a circle, then the hypotenuse is a diameter of the circle.

12. O G D Therefore, is a diameter of the circle.

13. Q U D A Theorem 10-11 • If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary. are supplementary are supplementary