Date post: | 17-Jan-2016 |
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Learning Target:
I can find the measures of central angles and arcs.
I can find circumference and arc length.
A CIRCLE is the set of all points equidistant from a given point
called the center.
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 piece of a circle’s circumference.
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.
AC
D
minor arcs
EO
AC
CE
DE
AD
AC
D
semicircles
EO
ACE
CAD
AC
D
major arcs containing point A
EO
ACD
CEA
DEA
ADC
AC
D
central angles containing D
EO
AOD
DOE
AC
D
radius
EO
AO
DO
EO
CO
AC
D
diameter
EO
AE
DC
The measure of a central angle is equal to its
intercepted arc.
53o
53o
O P
R
m ROP = 53°
m RP = 53°
Find the measure of each arc.
1. BC = 32 °
2. BD = 90 °
3. ABC = 180 °
4. AB = 148 °
1. BC =
2. BD =
3. ABC =
4. AB =
The circumference of a circle is the distance around the
outside of the circle.
or
The arc length of a circle is the length of an arc; a piece of the
circumference.
or
Concentric Circles are circles within the same plane (coplanar) that have
the same center.