11.3: INSCRIBED ANGLESObjectives: Students will be able to…• Apply the relationship between an inscribed angle

and the arc it intercepts• Find the measures of an angle formed by a

tangent and a chord

Inscribed Angle Theorem• Inscribed Angle: sides are chords, vertex is on the circle

THEOREM:

The measure of an inscribed angle is half the measurement of the intercepted arc ABAPBm

2

1

ABAPBm2

1

Find the value of each variable.

108°c°

a°b°

60°

Corollaries to Inscribed Angle Theorem

1. 2 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.

Find the values of the variables

d°

a°

b°c° 100°

99° 96°

Find the value of the variables

1. 2. [

40°

a°

P is the center of the circle.

P a°

b°

Theorem

The measure of an angle formed by a tangent and a chord is half the measure of the intercepted arc

Example: Find x.

Find the value of a.

a°

300°