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## 10.3 Inscribed Angles

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**Definitions**• Inscribed Angle – An angle whose vertex is on a circle and whose sides contain chords of the circle • Intercepted Arc – the arc that lies in the • interior of an inscribed angle and has • endpoints on the angle (arc AB)**Theorems**• If an angle is inscribed in a circle, then its measure is half the measure of the intercepted arc. • m < APB = ½ AB • m < APB = 60**Theorems**• If two inscribed angles of a circle intercept the same arc, then the angles are congruent. • m<DCR = m<RAD**Theorems**3. If a right triangle is inscribed in a circle, then the hypotenuse is a diameter of the circle.**Last Theorem!!!!**4. A quadrilateral can be inscribed in a circle if and only if its opposite sides are supplementary.**Examples**• Find the measure of arc TR • 260 • Find the m<DIS • 21**Last Example**3. Find the measure of angle D and angle W**Homework**• P. 617 9-23all