www.iTutoring.com -­‐ NOTES Central Angles and Arcs Name _________________________________ Date ___________________ Period _______ W
Central Angle
A central angle is an angle whose vertex is at
the center of the circle.
X
!VAW is a central angle.
Sum of Central Angles
The sum of all central angles within a
circle is 360º.
central
angle
A
V
Y
Z
W
Central Angle
A central angle is an angle whose vertex is at
the center of the circle.
X
!VAW is a central angle.
Sum of Central Angles
The sum of all central angles within a
circle is 360º.
V
85º
A
70º
90º
95º
Y
Z
minor arc
W
X
Arc
An arc is an unbroken piece of a circle.
A minor arc is an arc that is less than a
semicircle.
VW is a minor arc.
A
V
Z
A major arc is an arc that is greater than a
semicircle.
major arc
Y
XYZ is a major arc.
W
The Measure of an Arc
The measure of an arc is equal to the
measure of its central angle.
m!VAW = mVW
V
90º A
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Central Angles and Arcs Pg. 2 W
Arc Addition Postulate
The measure of two adjacent arcs is the sum
of the measures of the two arcs.
mVW + mWX = mVWX
X
45º
A
90º
V
W
90º
Arc Length
The arc length is the linear distance around
the circle of the arc.
B
90º A
mVW = mCB
length of VW ≠ length of CB
Arc Length =
V
C
mArc
(2πr)
360º
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Central Angles and Arcs Pg. 3 W
Find the arc length of CB and VW
B
V
Arc Length =
6 cm
C
90º A
4 cm
mArc
(2πr)
360º
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Central Angles and Arcs Pg. 4