Hello! Hope this helps :)
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:
Now we need to find the angle of APC:
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 :)
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