1. Find the measure of each arc.
Warm Up
Find the measure of each arc. JK JL
JML
JMK M N
68°
41° L J K

2. Circumference and Arc Length
Geometry

3. Circumference
The circumference of a circle is the distance around the circle.

4. Theorem Circumference of a Circle
The circumference C of a circle is C = πd or C = 2πr, where d is the diameter and r is the radius of the circle.

5. Example Solve for a stool with a circular seat.
Find the circumference of a seat with a radius of 9in.
Find the radius of the seat with a circumference of 52in.

6. Arc Length
An arc length is a portion of a circumference of a circle. You can use the measure of the arc (in degrees) to find its length (in linear units).

7. ARC LENGTH COROLLARY

8. Find the length of arc JK.
Example
Find the length of arc JK. M
60°
16 in. J K

9. Find the length of arc LM.
Example
Find the length of arc LM. L M
120°
8 in. K

10. Find the length of arc RS.
Example
Find the length of arc RS. R
7 cm Q
45° S

11. Shortcuts
The length of a semicircle is one half the circumference, and the length of a 90 degree arc is one quarter of the cirumference

12. Find the length of arc DG.
Example
Find the length of arc DG. D G O
14 in.

13. Diameter BC is 17 in. long. Find the length of arc BDC.
Example
Diameter BC is 17 in. long. Find the length of arc BDC. B D A C

14. Find the length of arc AMT.
Example
Find the length of arc AMT. A T H
34 mm M

15. Using Arc Lengths

16. Find the mTUV if the arc length of TUV is 27 ft.
Using Arc Lengths
Find the mTUV if the arc length of TUV is 27 ft. U T S
6.3 ft V

17. Find the length of the radius.
Using Arc Lengths
Find the length of the radius. B
7.64 m A
60° C

18. Find the indicated measure. a) mLM b) circumference
Using Arc Lengths
Find the indicated measure. a) mLM b) circumference
16.76 in. R M L
10.2 cm
8 in. Q
45° K S