10.6 Circles
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10.6 Circles. and. Arcs. 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. Central angle.

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10.6 Circles

and

Arcs

Objective: Find the measures

of central angles and arcs.


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A CIRCLEis 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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Central angle

A CENTRAL ANGLEof a circle is an angle with its vertex at the center of the circle.


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Arc

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


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Semicircle ABC

m ABC = 180

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

C

P

B

A


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

less than 180

more than 180


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LMN is a major arc. mLMN =

360 – mLN

RS is a minor arc.

mRS = m RPS.

S

P

R

N

O

M

L


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Identify the following in circle O:

1) the minor arcs

C

A

O

E

D


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Identify the following in circle O:

2) the semicircles

C

A

O

E

D


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Identify the following in circle O:

3) the major arcs containing point A

C

A

O

E

D


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R

53o

53o

P

O

The measure of a central angle is equal to its intercepted arc.


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Find the measure of each arc.

  • BC = 32

  • BD = 90

  • ABC = 180

  • 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.

  • Sleep

  • Food

  • Work

  • Must Do

  • Entertainment

  • Other


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THE END their time. Find the measure of each central angle in degrees.

Homework:

page 569 (1 – 26)