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