12.3 Inscribed Angles

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”

Theorem 12-9: Inscribed Angle Theorem

• The measure of an inscribed angle is equal to half of its intercepted arcs.

CAmBm

2

1

B

A

C

Examples

Find m<ABC Find m<ABC and m<ABD

Examples

Find m<DEF and mAEC Find m<ABC

3 inscribed < corollaries (thm sheet)

Theorem 12-10The measure of an angle formed by a chord and a

tangent is equal to half the measure of the intercepted arc.

B

D

C C

BD

mBDCCm2

1

Ex: find the numbered

angles.

1 2

108˚

32˚

1

161˚

12102˚

46˚