and Objective : Find the measures of central angles and arcs.
and
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
A CENTRAL ANGLE of a circle is an angle with its vertex at the
center of the circle.
Central angle
An arc is a part of a circle. In this case it is the part Pacman would
eat.
Arc
One type of arc, a semicircle, is half of a circle.
P
A
C Semicircle ABC
m ABC = 180
B
A minor arc is smaller than a semicircle. A major arc is greater than a semicircle.
R
S
P
L
N
M
RS is a minor arc.
mRS = m RPS.
O
LMN is a major arc. mLMN =
360 – mLN
AC
D
Identify the following in circle O:
1) the minor arcs
EO
AC
D
Identify the following in circle O:
2) the semicircles
EO
AC
D
Identify the following in circle O:
3) the major arcs containing point A
EO
The measure of a central angle is equal to its
intercepted arc.
53o
53o
O P
R
Find the measure of each arc.
1. BC = 32
2. BD = 90
3. ABC = 180
4. AB = 148
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
Homework:
page 569 (1 – 26)