10.notebook
April 15, 2014
10.6 Circles: Circumference and Arc Length
Terms to know: Concentric circles: two circles that lie in the same plane and have the same center.
Congruent arcs: are arcs that have the same measure and are in the same circle or in congruent circles.
Circumference of a Circle The circumference of a circle is π times the diameter.
d
r
Examples:
What is the radius of a circle with circumference 18π m? The radii of two concentric circles are 4.5 cm and 5.2 cm. How much greater is the circumference of the larger circle than that of the smaller circle. Leave your answer in term of π.
Apr 14­12:02 PM
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10.notebook
April 15, 2014
Arc Length (Theorem 5‐11 )
The length of an arc of a circle is the product of the ratio and the circumference of the circle. A
r
o
B
Examples: Leave your answer in term of π.
Find the length of a semicircle with radius 1.3 m.
The diameter of a circle is 12 cm.
Apr 14­12:03 PM
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10.notebook
April 15, 2014
10.6 Circles and Arcs
Continued
Objective: Be able to find the measures of central angles and arcs and to be able to calculate circumference and arc length.
Vocabulary:
Circle: the set of all points in a plane that are a given distance, the radius, from a given point, the center. Named using the Center Point.
Diameter: a segment that contains the center of the circle and whose endpoints are on the circle.
Radius: an segment with one endpoint on the circle and the other endpoint at the center of the circle. The Radius is half the length of the diameter.
Central Angle: is an angle whose vertex is the center of the circle.
Apr 11­12:15 PM
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Name the following:
1.) The Circle
A
C
B 2.) A diameter
3.) A radius
D
4.) A central angle
Apr 11­12:22 PM
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April 15, 2014
An arc is a part of a circles circumference measured in
degrees.
Minor arc
Semicircle
Y
D
B
A
major arc
R
C
S
A
A
Z
A semicircle is half the A minor arc is smaller than a
circle's circumference. semicircle so the measure
The measure is always must be less than 180
180
Use 2 points on the Use 3 points on the circle to name circle to name X
A major Arc is larger
than a semicircle so the
measure must be more
than 180
Use 3 points on the circle to name Apr 11­12:24 PM
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10.notebook
April 15, 2014
Arc Measure
The measure of a minor arc is equal to the measure of its corresponding central angle.
The measure of a major arc is the measure of the related minor arc subtracted from 360.
The measure of a semicircle is 180.
X
Y
W
50
Z
Apr 11­12:36 PM
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10.notebook
April 15, 2014
With a Partner Complete
Practice 10.6
Apr 11­12:36 PM
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