10.6 Circles

and

Objective: Find the measures

of central angles and arcs.

A CIRCLE is the set of all points equidistant from a given point

called the center.

This is circle P for Pacman.

Circle P

P

A CENTRAL ANGLE of a circle is an angle with its vertex at the

center of the circle.

Central angle

An arc is a part of a circle. In this case it is the part Pacman would

eat.

Arc

One type of arc, a semicircle, is half of a circle.

P

A

C Semicircle ABC

m ABC = 180

B

A minor arc is smaller than a semicircle. A major arc is greater than a semicircle.

R

S

P

L

N

M

RS is a minor arc.

mRS = m RPS.

O

LMN is a major arc. mLMN =

360 – mLN

AC

D

Identify the following in circle O:

1) the minor arcs

EO

AC

D

Identify the following in circle O:

2) the semicircles

EO

AC

D

Identify the following in circle O:

3) the major arcs containing point A

EO

The measure of a central angle is equal to its

intercepted arc.

53o

53o

O P

R

Find the measure of each arc.

1. BC = 32

2. BD = 90

3. ABC = 180

4. AB = 148

Here is a circle graph that shows how people really spend their time.

Find the measure of each central angle in degrees.

1. Sleep

2. Food

3. Work

4. Must Do

5. Entertainment

6. Other

Homework:

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