Warm Up

Find the measure of each arc.

1.JK

2.JL

3.JML

4.JMK

M

N

JK

L

68°

41°

11.4 Circumference and Arc Length

Geometry

Circumference

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

Theorem 11.6Circumference of a Circle

The circumference C of a circle is C = πd orC = 2πr, where d is the diameter and r is the radius of the circle.

Example

Solve for a stool with a circular seat.

a) Find the circumference of a seat with a radius of 9in.

b) Find the radius of the seat with a circumference of 52in.

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).

ARC LENGTH COROLLARY

Example

Find the length of arc JK.

M

J K

60°16 in.

Example

Find the length of arc LM.

K

LM

120°8 in.

Example

Find the length of arc RS.

Q

S

R

45°

7 cm

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

Example

Find the length of arc DG.

OG

D

14 in.

Example

Diameter BC is 17 in. long.Find the length of arc BDC.

A

C

B

D

Example

Find the length of arc AMT.

HT

A

34 mm

M

Using Arc Lengths

Using Arc Lengths

Find the mTUV if the arc length of TUV is 27 ft.

TU

V

S

6.3 ft

Using Arc Lengths

Find the length of the radius.

A

C

B

60° 7.64 m

Using Arc Lengths

Find the indicated measure.a) mLM b) circumference

Q

S

R

45° 10.2 cm

K

ML

16.76 in.

8 in.