1. Inscribed Angles
Notes and Examples

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. C B

4. Examples
Find m<ABC
Find 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 B D D C C

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