We are looking for the arc length of AC, and will need to use proportions to solve this. We need to find the angle of APC to figure out the length.

First, let's find the circumference of the entire circle, since we are finding a length of a portion of it:

Circumference=2*pi*radius

radius=(1/2)*24=12

Circumference=2*pi*12

C=24pi

Now we need to find the angle of APC:

Angle APB=180

Angle CPB=30

Angle APC=APB-CPB

Angle APC=180-30=150 degrees

Okay, so we know that angle APC=150 degrees, angle of a circle=360 degrees, circumference of circle=24pi. We can use these three numbers to determine length of AC:

angle of APC / angle of circle = length of AC / circumference of circle

150/360 = length of AC / 24pi

length of AC = 10pi

Let me know if you have any questions :)

May 19th, 2015

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