1. 7.6: Circles and Arcs Objectives:
To find the measures of arcs and central angles
To find the circumference and arc length

2. Central Angles and Arcs
The measure of an arc (in degrees) is equal to the measure of the central angle that intersects that arc m CB = 54° What is m BAC ? What is the measure of a semicircle?
54°

3. Find the indicated measures
Given: Circle E
Find: a.) b.) m AB c.) d.) m BCA B A E
120° C D

4. Inscribed Angles:
The vertex of the angle is ON the circle:

5. Examples:
1. Find
2. Find m AB

6. What are the measures of the central angles?

7. The number pi: An irrational number: non-repeating, non-terminating
It is the ratio of the circle’s circumference to its diameter
APPROXIMATE using 3.14, 22/7 or pi button on calculator
When asked to leave answer in terms of pi, LEAVE IN YOUR ANSWER. It is the exact value. No need to use pi button or 3.14, etc..

8. Circumference The distance around a circle CIRCUMFERENCE = or
d = diameter, r = radius
If given diameter, use the first formula, if given radius, use the second.

9. Find the circumference. Leave your answer in terms of pi.
300 yd

10. The diameter of a bicycle wheel is 22 in
The diameter of a bicycle wheel is 22 in. To the nearest whole number, how many revolutions does the wheel make if the bike travels 100 ft?
Find the circumference: How far does one revolution travel? Convert to feet: Divide 100 ft by answer:

11. Concentric Circles
How much longer is the distance around the outer circle than the inner?
30 ft
6 ft

12. ARC LENGTH: A fraction of the circle’s circumference
If an arc measures 60⁰, what fraction of the circle would it be? THEOREM: Length of arc = measure of arc • circumference of circle 360

13. A
length AB = m AB • 360 r B

14. Find the length of each arc: Leave your answer in terms ofAB
2. ADB B A
10 ft
18 cm
60⁰
150⁰ A D B

15. Arc Length vs. Arc Measure
How long is the arc
Measured in ft, in, cm, etc..
Fraction of the circumference
Often given in terms of pi
If you were to straighten out a circle, it would be a straight line. Arc length would be the length of a segment cut off that line
Measured in degrees
How many degrees does the arc take up on the circle
Same measure as the central angle.