1. UNIT 5
Circles

2. 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)

3. 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)

4. Identify: Semicircles  ________________________________
Minor Arcs  ________________________________
Major Arcs  ________________________________ B C E
BONUS
What’s the name of the circle?? A D

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

6. EX. 1 a) 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

7. EX. 1 (YOU TRY) B) Find the measure of each arc in Q.
mDC: ___________
mEB: ___________
mDAC: ___________
mACD: ___________ Q C A
35°
75° E D

8. 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.

9. CIRCLE FORMULAS C = πd or C = 2πr Why are these equations the same??
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??

10. Ex. 2 Find the circumference and area of each . (Fill in the blanks)
2.3 cm
3 in.
5 in.
C = πd
C = π(15)
C = 47.1 m
A = πr2
A = π(7.5)2
A = 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

11. 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