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Geometry
Arcs and Central Angles
May 23, 2017
Symbols
 Circle
 Arc
May 23, 2017
Goals
 Identify arcs & central angles in
circles
 Compute arc measures and angle
measures
May 23, 2017
Central Angle
A
May 23, 2017
An angle whose
vertex is the
center of a
circle.
Minor Arc
C
Part of a circle.
The measure of
the central
T angle is less
than 180.
A
CT
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Semicircle
C
A
D
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Half of a circle. The
endpoints of the arc
are the endpoints of
a diameter. The
central angle
T
measures 180.
CTD
Major Arc
C
A
D
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T
Part of a circle.
The measure of
the central
angle is greater
than 180.
CTD
Major Arc
C
CTD
BUT NOT
A
D
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T
CDT
Measuring Arcs
 An arc has the same measure as the
central angle.
 We say, “a central angle subtends an arc
of equal measure”.
mACB  42
A
42
42
C
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B
mAB  42


Measuring Major Arcs
 The measure of an major arc is given by
360  measure of minor arc.
mACB  42
A
42
42
D
C
B
mAB  42


mADB  360  42  318

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

Arc Addition Postulate
R
T
C
A
mRAT  mRA  mAT
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What have you learned so far?






1) mRS  60
2) mRPS 300
3) mPQR180
4) mQS 100
5) mQSP 220
6) mQTR  40
Q
T
60
S
P
120
May 23, 2017
40
R
Homework
May 23, 2017