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### UNIT 5

Circles

Key Term (only write what’s in RED)

- Circle: the set of a all points that are a given distance from a given point called the center
KEEP IN MIND:

A circle is a shape with all points the same distance from its center. A circle is named by its center. Thus, the circle below is called circle A since its center is at point A. Some real world examples of a circle are a wheel, a dinner plate and (the surface of) a coin.

written as: A (circle A)

Key Terms

Do you remember…?

- Arc: part of the circumference of a circle
- Semicircle: half of a circle (180°)
- Minor Arc: smaller than a semicircle (2 letters)
- Major Arc: greater than a semicircle (3 letters)

Identify:

- Semicircles ________________________________
- Minor Arcs ________________________________
- Major Arcs ________________________________

B

C

E

BONUS

What’s the name of the circle??

A

D

*the measure of an arc is EQUAL to the measure of its CENTRAL ANGLE

EX. 1a) Find the measure of each arc in Q.

mCD: 40°

mAD: 180° - 40° = 140°

mCAD: 360° - 40° = 320°

or 140° + 180° = 320°

mDCA: 360° - 140° = 220°

or 180° + 40° = 220°

D

40°

A

C

Q

EX. 1 (YOU TRY)B) Find the measure of each arc in Q.

B

mDC: ___________

mEB: ___________

mDAC: ___________

mACD: ___________

Q

C

A

35°

75°

E

D

Parts of a Circle

KEEP IN MIND:

The distance across a circle through the center is called the diameter. A real-world example of diameter is a 9-inch plate.

The radius of a circle is the distance from the center of a circle to any point on the circle. If you place two radii end-to-end in a circle, you would have the same length as one diameter. Thus, the diameter of a circle is twice as long as the radius.

A chord (pronounce CORD) is a line segment that joins two points on a curve. In geometry, a chord is often used to describe a line segment joining two endpoints that lie on a circle. The circle to the top right contains chord AB.

CIRCLE FORMULAS

CIRCUMFERENCE

AREA

- C = πd
or

- C = 2πr
Why are these equations the same??

- A = πr×r
or

- A = πr2
Why are these equations the same??

Ex. 2Find the circumference and area of each .(Fill in the blanks)

2.3 cm

15m

3 in.

5 in.

C = πd

C = π(15)

C = 47.1 m

A = πr2

A = π(7.5)2

A = 176. 7 m2

*hint: use PT

C = πd

C = π( ____ )

C = _____cm

A = πr2

A = π(2.3)2

A = 16.6 cm2

C = πd

C = π( ____ )

C = _____ in.

A = πr2

A = π( ____ )2

A = _______in2

Ex. 3)

The diameter of a bicycle wheel is 17 inches. If the wheel makes 10,500 revolutions, how far did the bike travel?

d = 17; C = πd

C = π(17)

C ≈ 53.4

For 1 revolution, the bike traveled about 53.4 in. To find the distance traveled for 10,500 revolutions, multiply:

C ≈ 53.4 × 10,500

C ≈ 560,774.3 inches

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