The document defines key terms related to circles such as central angle, arc, semicircle, minor arc, and major arc. It provides examples of identifying these elements in circles and finding the measures of central angles and arcs. The document concludes with homework problems involving calculating measures of central angles and arcs in various circle graphs and diagrams.

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

2. 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.
Central angle

4. 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.
P
A
C Semicircle ABC
m ABC = 180
B

6. A minor arc is smaller than
a semicircle.

7. A major arc is greater than
a semicircle.

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

9. R
S
P
RS is a minor arc.
mRS = m RPS.

10. L
N
M O
LMN is a major arc.
mLMN = 360 – mLN

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

12. A
C
D
Identify the following in circle O:
1) the minor arcs
EO

13. A
C
D
Identify the following in circle O:
1) the minor arcs
EO
AD

14. A
C
D
Identify the following in circle O:
1) the minor arcs
EO
AD, CE

15. A
C
D
Identify the following in circle O:
1) the minor arcs
EO
AD, CE, AC,

16. A
C
D
Identify the following in circle O:
1) the minor arcs
EO
AD, CE, AC, & DE

17. A
C
D
Identify the following in circle O:
1) the minor arcs
EO
AD, CE, AC, & DE

18. A
C
D
Identify the following in circle O:
2) the semicircles
EO

19. A
C
D
Identify the following in circle O:
2) the semicircles
EO
ACE

20. A
C
D
Identify the following in circle O:
2) the semicircles
EO
ACE, CED

21. A
C
D
Identify the following in circle O:
2) the semicircles
EO
ACE, CED, EDA

22. A
C
D
Identify the following in circle O:
2) the semicircles
EO
ACE, CED, EDA, & DAC

23. A
C
D
Identify the following in circle O:
2) the semicircles
EO
ACE, CED, EDA, & DAC

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

25. A
C
D
Identify the following in circle O:
3) the major arcs containing
point A
EO
ACD

26. A
C
D
Identify the following in circle O:
3) the major arcs containing
point A
EO
ACD, CEA

27. A
C
D
Identify the following in circle O:
3) the major arcs containing
point A
EO
ACD, CEA, EDC

28. A
C
D
Identify the following in circle O:
3) the major arcs containing
point A
EO
ACD, CEA, EDC,& DAE

29. A
C
D
Identify the following in circle O:
3) the major arcs containing
point A
EO
ACD, CEA, EDC,& DAE

30. The measure of a central
angle is equal to its
intercepted arc.
53o
53o
O
P
R

31. The measure of a central
angle is equal to its
intercepted arc.
53o
53o
O
P
R

32. Find the measure of each arc.
1. BC =
2. BD =
3. ABC =
4. AB =

33. Find the measure of each arc.
1. BC = 32
2. BD =
3. ABC =
4. AB =

34. Find the measure of each arc.
1. BC = 32
2. BD =
3. ABC =
4. AB =

35. Find the measure of each arc.
1. BC = 32
2. BD = 90
3. ABC =
4. AB =

36. Find the measure of each arc.
1. BC = 32
2. BD = 90
3. ABC = 180
4. AB =

37. Find the measure of each arc.
1. BC = 32
2. BD = 90
3. ABC = 180
4. AB = 148

38. 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

39. 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

40. 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

41. 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

42. 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

43. 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

44. 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

45. 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

46. 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

47. 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

48. Homework:
page 569 (1 – 26)