Unit 9: Circles
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Section 9.1 : Circles
A circle is defined as the set of all points in a plane that are equidistant from a given fixed point called the center.
­A circle is named by its center.
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Ab
Which of the following is a circle? Explain.
b
a
F
a
a=b
F
b
a≠b
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Parts of the Circle:
radius AB
A
Radius: segment from the center to edge
radius = 1/2 ﴾diameter﴿
2﴾radius﴿ = diameter
B
diameter CB
Diameter: chord that contains the center; Longest chord of the circle
radius = 1/2﴾diameter﴿
2﴾radius﴿ = diameter
A
.
C
D
Chord: segments whose endpoints
are on the circle
Congruent Circles:
A
B
chord DB
B
Circles are congruent if they have the same radius.
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G
C
A
Practice:
E
D
B
H
F
a.﴿ Name of circle?
a.﴿ What is the name of this circle?
b.﴿ Radius?
b.﴿ What is the radius?
c.﴿ Diameter?
c.﴿ What is the diameter?
d.﴿ What is CG?
d.﴿ What is EH?
e.﴿ If AD is 2 units, and BF is 4 units, are these congruent circles?
Why or Why not?
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Area of a Circle
The formula for the area of a circle is the following:
Area = πr
B
r
2
radius
What is
a radius?
5
Example 1
Find the area of the circle M.
4
M
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Example 2
Find the area of the circle P if d = 10.
P
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Circumference of a Circle
The formula for the circumference of a circle is the the perimeter of a circle;
following:
the outer boundary
Circumference =πd
diameter
d
What is
a diameter?
B
8
Example 3
Find the circumference of the circle R if d =8.
R
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Example 4
Find the circumference of the circle S.
6
S
10
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D
A
P
B
1. Name the center of circle P.
2. Name three radii of the circle.
3. Name a diameter.
4. Name two chords.
5. If AP = 4, find AB.
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Equation for Circles: ﴾x­h﴿2 + ﴾y­k﴿2 = r2
* x and y stay as variables!
* ﴾h,k﴿ is the center
h, k, and r are * r is the radius
numbers!
Example 5: Write an equation for the circle having the given center and radius or diameter:
a﴿ ﴾6,0﴿ r = 3
b﴿ ﴾4, 6﴿ d = 18
c﴿ ﴾2, ­3﴿ d = 10
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Example 6
The equation of circle L is: ﴾x + 3﴿2 = 8 ­ ﴾y ­3﴿2
Center:___________
Radius:___________
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Example 7
x + y = 9
2
2
Center:___________
Radius:___________
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Write an equation for the circle.
6. ﴾2,3﴿ r = 5
7. ﴾1,­4﴿ d = 8
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