Section 10.3 Inscribed Section 10.3 Inscribed AnglesAngles

GeometryGeometry

April 10, 2004April 10, 2004

Find the measure of the angle.Find the measure of the angle.

196

CB

A

D

mABC

= ½ (196)

= 98

Theorem 10.9Theorem 10.9

If two inscribed If two inscribed angles of a circle angles of a circle intercept the same intercept the same arc, then the angles arc, then the angles are congruent.are congruent. J = J = KK

I

J

K

L

HomeworkHomework

p.619 (9-23)p.619 (9-23)

Inscribed AnglesInscribed Angles

Inscribed AngleInscribed Angle – an – an angle whose vertex is angle whose vertex is on a circle and whose on a circle and whose sides contain chords sides contain chords of the circleof the circle Intercepted arc – an Intercepted arc – an

arc that lies on the arc that lies on the interior of an inscribed interior of an inscribed angleangle

inscribed angle

intercepted arc

Measure of an Inscribed AngleMeasure of an Inscribed Angle

If an angle is If an angle is inscribed in a circle, inscribed in a circle, then its measure is then its measure is half the measure of its half the measure of its intercepted arc.intercepted arc. mmADB = ½ mABADB = ½ mAB

A

B

CD

Find the measure of each arc or Find the measure of each arc or angle.angle.

C

B

A

D

1.m ADC

= 180