Lesson 9.2AR.4.G.5 Investigate and use the properties of angles (central and inscribed) arcs, chords, tangents, and

secants to solve problems involving circles

Intercepted ArcA piece of a circle contained between the two rays of an angle

Central AngleAn angle inside a circle with its vertex at the center of the circle

Inscribed AngleAn angle inside a circle with its vertex on the circle

• Arc measures always given in degrees.

• The measure of a central angle is equal to the measure of the intercepted arc.

• The measure of the inscribed angle is one half of the measure of the intercepted arc.

• A tangent line is always perpendicular to the radius or diameter drawn to the point of tangency.

Find the value of the variables:

xo

A

C

B

xo

AC

B

30O

Find the value of the variables:

150o

AB

xO

yo

AC

B60O

Given that AB is tangent to the circle, find the value of x.

37o

xo

A

BC

Given that CD is tangent to the circle, find the value of x.

xo

72oC

D

E

Given that AB and AD are both tangent to the circle, find the value of x.

140o

xoA

B

D

C

Given that PQ and PS are both tangent to the circle, find the value of x.

150o

xoP

Q

S

T

Remember, the radius of a circle never changes, regardless of what point on the circle it’s drawn to.

Find the value of x, given circle O and the following segment lengths: AC = 16, OB = 12, OE = x. If your answer is not an integer, round to the nearest tenth.

x

A CB

O

E

Find the value of x, given circle O and the following segment lengths: AC = 50, OB = 20, OE = x. If your answer is not an integer, round to the nearest tenth.

x

A CB

O

E

Find the value of x, given circle P and the following segment lengths: MN = 35, PS = 10, ST = x. If your answer is not an integer, round to the nearest tenth.

M N

S

P

T

Find the value of x, given circle P and the following segment lengths: MN = 18, PS = 5, ST = x. If your answer is not an integer, round to the nearest tenth.

M

N

S

P

T