11.4 Inscribed Angles. New Vocab: Inscribed Angle and Intercepted Arc.

11.4

Inscribed Angles

New Vocab: Inscribed Angle and Intercepted Arc

Notice anything cool?1. Draw a

diameter.2. Put 3 more

points anywhere on the circle.

3. Make triangles.

What is the measure of all the inscribed angles when they are connected to a diameter? ______

Measure of an Inscribed Angle

The measure of an inscribed angle is ____ the measure of its intercepted arc.

yx

55H I

J

Theorem If two inscribed angles of a circle intercept

the same arc, then the angles are _____.

120

yx

Theorem A quad that is inscribed in a circle (called a

“cyclic quad”) has opposite angles that are ___________________.

58

pq

Examples: Find the variable values

z x

11272

y

Tangent-Chord If a tangent and a chord intersect at a point on a

circle, then the measure of each angle formed is __________ the measure of its intercepted arc.

12

B

A

CIf <1=60⁰, then arc AB=______

(different problem)

If arc ACB=256⁰, then <2=_______.

Put it all together…

mBAC =

132O

B

C

A

mGHI =

m GH =

94E

G

H

I

J

Find x

2x+13

3x