unit 9: circles · 2 think about it! f a b a=b b a f a≠b which of the following is a circle?...

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Unit 9: Circles

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Think

About I

t!

Fa

b

a=b

b

aF

a≠b

Which of the following is a circle? Explain.

Section 9.1 : CirclesA 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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Radius: segment from the center to edge radius = 1/2 ﴾diameter﴿ 2﴾radius﴿ = diameter

AB

radius ABParts of the Circle:

chord that contains the center; Longest chord of the circle radius = 1/2﴾diameter﴿ 2﴾radius﴿ = diameter

Diameter:

C B.

diameter CB

A

Chord: segments whose endpoints are on the circle

A B

chord DBD

Congruent Circles: Circles are congruent if they have the same radius.

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AC D

G

B

E

FHa.﴿ Name of circle?

b.﴿ Radius?

c.﴿ Diameter?

d.﴿ What is CG?

a.﴿ What is the name of this circle?

b.﴿ What is the radius?

c.﴿ What is the diameter?

d.﴿ What is EH?

e.﴿ If AD is 2 units, and BF is 4 units, are these congruent circles?Why or Why not?

Practice:Practice:

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Area of a CircleThe formula for the area of a circle is the following:

B rradius

Area = πr2

What isa radius?

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Example 1

M

4

Find the area of the circle M.

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Example 2Find the area of the circle P if d = 10.

P

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Circumference of a CircleThe formula for the circumference of a circle is the following:

diameter

Circumference =πd

B

d What isa diameter?

the perimeter of a circle;the outer boundary

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Example 3Find the circumference of the circle R if d =8.

R

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Example 4Find the circumference of the circle S.

S

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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.

AP

B

D

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Equation for Circles: ﴾x­h﴿2 + ﴾y­k﴿2 = r2

* x and y stay as variables!* ﴾h,k﴿ is the center* r is the radius h, k, and r are

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 6The equation of circle L is:

﴾x + 3﴿2 = 8 ­ ﴾y ­3﴿2

Center:___________

Radius:___________

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Example 7 x2 + y2 = 9Center:___________

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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