1. 12.3 Inscribed Angles

2. Vocab: inscribed angle - an angle whose vertex is on a circle and whose sides are chords <ABC and <DEF are inscribed angles in the circles shown below: <ABC intercepts minor arc AC <DEF intercepts major arc DGF *intercept means “forms”

3. Theorem 12-9: Inscribed Angle Theorem The measure of an inscribed angle is equal to half of its intercepted arcs. B A C

4. Examples Find m<ABCFind m<ABC and m<ABD

5. Examples Find m<DEF and mAEC Find m<ABC

6. 3 inscribed < corollaries (thm sheet) If two inscribed angles intercept the same arc, then the angles are congruent. An angle inscribed in a semicircle is a right angle. If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary.

7. Theorem 12-10 The measure of an angle formed by a chord and a tangent is equal to half the measure of the intercepted arc. B D CC B D

8. Ex: find the numbered angles. 12 108˚ 32˚ 1 1 61˚ 1 2 102˚ 46˚