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.

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

R

SP

RS is a minor arc.

mRS = m RPS.

L

N

M O

LMN is a major arc.

mLMN = 360 – mLN

R

SP

L

N

M

RS is a minor arc.

mRS = m RPS.

O

LMN is a major arc.

mLMN = 360 – mLN

A C

D

Identify the following in circle O:

1) the minor arcs

EO

A C

D

Identify the following in circle O:

1) the minor arcs

EO

AD

A C

D

Identify the following in circle O:

1) the minor arcs

EO

AD, CE

A C

D

Identify the following in circle O:

1) the minor arcs

EO

AD, CE, AC,

A C

D

Identify the following in circle O:

1) the minor arcs

EO

AD, CE, AC, & DE

A C

D

Identify the following in circle O:

1) the minor arcs

EO

AD, CE, AC, & DE

A C

D

Identify the following in circle O:

2) the semicircles

EO

A C

D

Identify the following in circle O:

2) the semicircles

EO

ACE

A C

D

Identify the following in circle O:

2) the semicircles

EO

ACE, CED

A C

D

Identify the following in circle O:

2) the semicircles

EO

ACE, CED, EDA

A C

D

Identify the following in circle O:

2) the semicircles

EO

ACE, CED, EDA, & DAC

A C

D

Identify the following in circle O:

2) the semicircles

EO

ACE, CED, EDA, & DAC

A C

D

Identify the following in circle O:

3) the major arcs containing point A

EO

A C

D

Identify the following in circle O:

3) the major arcs containing point A

EO

ACD

A C

D

Identify the following in circle O:

3) the major arcs containing point A

EO

ACD, CEA

A C

D

Identify the following in circle O:

3) the major arcs containing point A

EO

ACD, CEA, EDC

A C

D

Identify the following in circle O:

3) the major arcs containing point A

EO

ACD, CEA, EDC,& DAE

A C

D

Identify the following in circle O:

3) the major arcs containing point A

EO

ACD, CEA, EDC,& DAE

The measure of a central angle is equal to its

intercepted arc.

53o

53o

O P

R

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 =

2. BD =

3. ABC =

4. AB =

Find the measure of each arc.

1. BC = 32

2. BD =

3. ABC =

4. AB =

Find the measure of each arc.

1. BC = 32

2. BD =

3. ABC =

4. AB =

Find the measure of each arc.

1. BC = 32

2. BD = 90

3. ABC =

4. AB =

Find the measure of each arc.

1. BC = 32

2. BD = 90

3. ABC = 180

4. AB =

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

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

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

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

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

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

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

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

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

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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