L.E.Q. How do you find the measures of
central angles and arcs?
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A circle is the set of all points equidistant
from a given point called the center.
You name a circle by its center. The circle
below is named “circle P”.
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Radius - a segment that has one endpoint at
the center and the other endpoint on the
circle.
Diameter - a segment that contains the
center of a circle and has both endpoints on
the circle.
Central Angle - an angle whose vertex is the
center of the circle.
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Congruent Circles have congruent radii.
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To learn how people really spend their time, a
research firm studied the hour-by-hour
activities of 3600 people. The participants
were between 18 and 90 years old. Each
participant was sent a 24-hour recording
sheet every March for three years from 2000
to 2002.

The study found that people spend most of
their time sleeping, working, and watching
television. Some information from the study
is shown in this circle graph. Find the
measure of each central angle in the circle
graph.
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An arc consists of 2 points on a circle and all
the points in between them.
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Semicircle – an arc that covers half the circle.
Major Arc – an arc that is larger than a
semicircle.
Minor Arc – an arc that is smaller than a
semicircle.
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The measure of an arc is equal to the
measure of its corresponding central angle,
the central angle that intersects the arcs
endpoints.
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Id. the following arcs in circle O.
◦ The minor arcs.
◦ The semicircles.
◦ The major arcs.
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Adjacent arcs are arcs of the same circle that
have exactly one point in common.
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The measure of the arc formed by two
adjacent arcs is the sum of the measures of
the two arcs.
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Pgs 389-390 #s 2 – 26 even.