10.5 Inscribed Angles An __________________________ has a vertex on a circle and sides that contain chords of the circle. The endpoints on the ends of an inscribed angle is an intercepted arc. Inscribed Angle Theorem If an angle is inscribed in a circle, then the measure of the angles equals one half the measure of its intercepted arc. Example 1: a) mDH b) m∠P c) Find m∠P and mPO. d) Find mCF and m∠C. Inscribed Polygons Triangles Quadrilaterals An inscribed angle of a triangle intercepts a If a quadrilateral is inscribed in a circle, then its diameter or semicircle if and only if the angle is opposite angles are supplementary. a right triangle. Example 2: a) b) Find the measure of angle X and Y. 10.5 HW 1. 2. 3.
10.5 Inscribed Angles An __________________________ has a vertex on a circle and sides that contain chords of the circle. The endpoints on the ends of an inscribed angle is an intercepted arc. Inscribed Angle Theorem If an angle is inscribed in a circle, then the measure of the angles equals one half the measure of its intercepted arc. Example 1: a) mDH b) m∠P c) Find m∠P and mPO. d) Find mCF and m∠C. Inscribed Polygons Triangles Quadrilaterals An inscribed angle of a triangle intercepts a diameter or semicircle if and only if the angle is a right triangle. If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary. Example 2: a) b) Find the measure of angle X and Y. 10.5 HW 1. 2. 3.