Transcript Ch 10.6 Circles and Arcs

10.6 Circles and Arcs
Essential Questions:
How do you find the measures of central angles and
arcs?
How do you find circumference and arc length?
• Circle: set of all points in a plane equidistant
from a given point called the center.
• You name a circle by its center.
• Radius: a segment that has one endpoint at the
center and the other endpoint on the circle.
• Congruent circles have congruent radii.
• Diameter: a segment that contains the center of
a circle and has both endpoints on the circle.
• Central angle: angle whose vertex is the center of
the circle.
Example 1
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An arc is a part of a circle.
One type of arc, a semicircle, is half of a circle.
A minor arc is smaller than a semicircle.
A major arc is greater than a semicircle.
Example 2
• Adjacent arcs: arcs of the same circle that
have exactly one point in common.
– You can add the measures of adjacent arcs just
like adding the measures of adjacent angles.
Example 3
• Circumference: the distance around the circle.
– The number pi (π) is the ratio of the
circumference of a circle to its diameter.
Example 4
• Concentric circles: circles in the same plane
and same center.
• Arc length: a fraction of a circle’s
circumference measured in degrees.
Example 5
• It is possible for two arcs of different circles to
have the same measure but different lengths.
• It is also possible for two arcs of different
circles to have the same lengths but different
measures.
• Congruent arcs: arcs equal in measure and in
the same circle or in congruent circles.
Summary
• Answer the essential questions in detailed,
complete sentences.
• How do you find the measures of central
angles and arcs?
• How do you find circumference and arc
length?
• Write 2-4 study questions in the left column
to correspond with the notes.