1. and Circles Arcs Objective: Find the measures
of central angles and arcs.

2. This is circle P for Pacman.
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

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

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

5. One type of arc, a semicircle, is half of a circle.
Semicircle ABC
m ABC = 180 P B A

6. A minor arc is smaller than a semicircle
A minor arc is smaller than a semicircle. A major arc is greater than a semicircle.
less than 180
more than 180

7. LMN is a major arc. mLMN = 360 – mLN R N S O P M L RS is a minor arc.
mRS = m RPS. R N S P O M L

8. Identify the following in circle O:
1) the minor arcs C A O E D

9. Identify the following in circle O:
2) the semicircles C A O E D

10. 3) the major arcs containing point A
Identify the following in circle O:
3) the major arcs containing point A C A O E D

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

12. Find the measure of each arc.
BC = 32
BD = 90
ABC = 180
AB = 148

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

14. THE END
Homework