1. and 10.6 Circles Arcs Objective: Find the measures
of central angles and arcs and the lengths of 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. Arc Addition Postulate
Adjacent arcs are arcs on the same circle that have exactly one point in common.
You can Add the Measure of Adjacent Arcs just as you can add the measures of adjacent angles.

15. Finding Arc Measure

16. Arc Length
The measure of an arc length is a fraction of the circles circumference.
The Fraction is based on a ratio of the measure of the central angle out of 360°

17. Finding Arc Length

18. Try Some More! Find the Arc Measure of AB and CD.
Find the Arc Length of AB and CD
What do you notice about the Arc Measure? The Arc Length?

19. Be Careful…
Two arcs can have the same Arc Measure but different Arc Lengths.
It is also possible for two arcs to have different Arc Measures but the same Arc Lengths.
Congruent Arcs have the same Arc Measure and Same Arc Length.

20. THE END
Homework:
10.6 P ,12-44 even, 47-56, 60-62