Lesson 81: Central Angles
and Arcs
GEOMETRY
Vocabulary
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Central angle: an angle whose vertex is the center of a circle
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The sum of central angle measures for any circle is 360°.
Arc: a portion of a circle intercepted by a central angle
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An arc that forms a half circle is called a semicircle.
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An arc that is smaller than a semicircle is a minor arc.
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An arc that is bigger than a semicircle is a major arc.
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Minor arcs are named with two points.
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Major arcs are named with three points.
The size of an arc is the same as the measure of its central angle.
Example
Draw a circle with central angles that divide the circle evenly into thirds.
Example
The court of a playground is painted on the blacktop. The court is formed by
a circle with two intersecting diameters, forming four central angles. One of
the central angles measures 50°. Find the measures of the other angles.
Example
What is the measure of each acute central angle?
What is the measure of arc CD?
What is the measure of major arc CD?
If the diameter of the circle is 20 cm, what is the length of arc CD?
C
D
Homework
LESSON 81: A-D, 5, 23,
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