Inscribed Angles Section 10-4

inscribed angle – an angle whose vertex is on the circle and whose sides each contain chords of the circle. ADC is an inscribed arc. A B C D

Inscribed Angle Thm (10.5) If an angle is inscribed in a circle, then the measure of the angle equals ½ the measure of its intercepted arc. 70 o 140 o

Theorem 10.6 If 2 inscribed angles of a circle or congruent circles intercept congruent arcs or the same arc, then the angles are congruent. A B C D

Theorem 10.7 If an inscribed angle of a circle intercepts a semicircle, then the angle is a right angle. 180 o

Theorem 10.8 If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary. 60 o 120 o

Joke Time What do you get if you take a native Alaskan and divide its circumference by its diameter? Eskimo pi

Why did Humpty Dumpty have a great fall? To make up for his miserable summer