11-3 Inscribed Angles Learning Target: I can solve problems using inscribed angles. Goal 2.03.

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Presentation transcript:

11-3 Inscribed Angles Learning Target: I can solve problems using inscribed angles. Goal 2.03

An angle is inscribed in a circle if the vertex of the angle is on the circle and the sides of the angle are chords of the circle.

An intercepted arc is an arc of a circle having endpoints on the sides of an inscribed angle, and its other points in the interior of the angle.

Inscribed Angle Theorem The measure of an inscribed angle is half the measure of its intercepted arc. m<B= mAC 1 _ 2

Corollaries to the Inscribed Angle Theorem 1. Two inscribed angles that intercept the same arc are congruent. 2. An angle inscribed in a semicircle is a right angle. 3. The opposite angles of a quadrilateral inscribed in a circle are supplementary.

Theorem The measure of an angle formed by a tangent and a chord is half the measure of the intercepted arc. m<C = mBDC 1 _ 2 B C D C B D