lesson 9.2a r.4.g.5 investigate and use the properties of angles (central and inscribed) arcs,...

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