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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:
page 569 (1 – 26)