CK-12 Geometry-Concepts

10.9. Arc Length http://www.ck12.org

In the picture, the central angle that corresponds withPQ̂is 60◦. This means thatmPQ̂= 60 ◦as well. So, think of
the arc length as a portion of the circumference. There are 360◦in a circle, so 60◦would be^16 of that

( 60 ◦

360 ◦=

1

6

)

.

Therefore, the length ofPQ̂is^16 of the circumference.

length o fPQ̂=

1

6

· 2 π( 9 ) = 3 π

Example B

The arc length ofAB̂= 6 πand is^14 the circumference. Find the radius of the circle.

If 6πis^14 the circumference, then the total circumference is 4( 6 π) = 24 π. To find the radius, plug this into the
circumference formula and solve forr.

24 π= 2 πr

12 =r

Example C

Find the measure of the central angle orPQ̂.

Let’s plug in what we know to the Arc Length Formula.

15 π=

mPQ̂

360 ◦

· 2 π( 18 )

15 =

mPQ̂

10 ◦

150 ◦=mPQ̂