10.6 circles and arcs
TRANSCRIPT
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and
Objective: Find the measures
of central angles and arcs.
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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
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A CENTRAL ANGLE of a circle is an angle with its vertex at
the center of the circle.
Central angle
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An arc is a part of a circle. In this case it is the part Pacman
would eat.
Arc
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One type of arc, a semicircle, is half of a circle.
P
A
C Semicircle ABC
m ABC = 180
B
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A minor arc is smaller than a semicircle.
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A major arc is greater than a semicircle.
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A minor arc is smaller than a semicircle. A major arc is greater than a semicircle.
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R
SP
RS is a minor arc.
mRS = m RPS.
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L
N
M O
LMN is a major arc.
mLMN = 360 – mLN
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R
SP
L
N
M
RS is a minor arc.
mRS = m RPS.
O
LMN is a major arc.
mLMN = 360 – mLN
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A C
D
Identify the following in circle O:
1) the minor arcs
EO
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A C
D
Identify the following in circle O:
1) the minor arcs
EO
AD
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A C
D
Identify the following in circle O:
1) the minor arcs
EO
AD, CE
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A C
D
Identify the following in circle O:
1) the minor arcs
EO
AD, CE, AC,
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A C
D
Identify the following in circle O:
1) the minor arcs
EO
AD, CE, AC, & DE
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A C
D
Identify the following in circle O:
1) the minor arcs
EO
AD, CE, AC, & DE
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A C
D
Identify the following in circle O:
2) the semicircles
EO
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A C
D
Identify the following in circle O:
2) the semicircles
EO
ACE
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A C
D
Identify the following in circle O:
2) the semicircles
EO
ACE, CED
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A C
D
Identify the following in circle O:
2) the semicircles
EO
ACE, CED, EDA
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A C
D
Identify the following in circle O:
2) the semicircles
EO
ACE, CED, EDA, & DAC
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A C
D
Identify the following in circle O:
2) the semicircles
EO
ACE, CED, EDA, & DAC
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A C
D
Identify the following in circle O:
3) the major arcs containing point A
EO
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A C
D
Identify the following in circle O:
3) the major arcs containing point A
EO
ACD
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A C
D
Identify the following in circle O:
3) the major arcs containing point A
EO
ACD, CEA
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A C
D
Identify the following in circle O:
3) the major arcs containing point A
EO
ACD, CEA, EDC
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A C
D
Identify the following in circle O:
3) the major arcs containing point A
EO
ACD, CEA, EDC,& DAE
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A C
D
Identify the following in circle O:
3) the major arcs containing point A
EO
ACD, CEA, EDC,& DAE
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The measure of a central angle is equal to its
intercepted arc.
53o
53o
O P
R
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The measure of a central angle is equal to its
intercepted arc.
53o
53o
O P
R
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Find the measure of each arc.
1. BC =
2. BD =
3. ABC =
4. AB =
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Find the measure of each arc.
1. BC = 32
2. BD =
3. ABC =
4. AB =
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Find the measure of each arc.
1. BC = 32
2. BD =
3. ABC =
4. AB =
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Find the measure of each arc.
1. BC = 32
2. BD = 90
3. ABC =
4. AB =
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Find the measure of each arc.
1. BC = 32
2. BD = 90
3. ABC = 180
4. AB =
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Find the measure of each arc.
1. BC = 32
2. BD = 90
3. ABC = 180
4. AB = 148
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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
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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
![Page 40: 10.6 circles and arcs](https://reader034.vdocuments.us/reader034/viewer/2022042607/55ae4f3d1a28abd7738b46fa/html5/thumbnails/40.jpg)
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
![Page 41: 10.6 circles and arcs](https://reader034.vdocuments.us/reader034/viewer/2022042607/55ae4f3d1a28abd7738b46fa/html5/thumbnails/41.jpg)
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
![Page 42: 10.6 circles and arcs](https://reader034.vdocuments.us/reader034/viewer/2022042607/55ae4f3d1a28abd7738b46fa/html5/thumbnails/42.jpg)
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
![Page 43: 10.6 circles and arcs](https://reader034.vdocuments.us/reader034/viewer/2022042607/55ae4f3d1a28abd7738b46fa/html5/thumbnails/43.jpg)
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
![Page 44: 10.6 circles and arcs](https://reader034.vdocuments.us/reader034/viewer/2022042607/55ae4f3d1a28abd7738b46fa/html5/thumbnails/44.jpg)
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
![Page 45: 10.6 circles and arcs](https://reader034.vdocuments.us/reader034/viewer/2022042607/55ae4f3d1a28abd7738b46fa/html5/thumbnails/45.jpg)
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
![Page 46: 10.6 circles and arcs](https://reader034.vdocuments.us/reader034/viewer/2022042607/55ae4f3d1a28abd7738b46fa/html5/thumbnails/46.jpg)
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
![Page 47: 10.6 circles and arcs](https://reader034.vdocuments.us/reader034/viewer/2022042607/55ae4f3d1a28abd7738b46fa/html5/thumbnails/47.jpg)
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
![Page 48: 10.6 circles and arcs](https://reader034.vdocuments.us/reader034/viewer/2022042607/55ae4f3d1a28abd7738b46fa/html5/thumbnails/48.jpg)
Homework:
page 569 (1 – 26)