Answer: 8pi
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Step-by-step explanation:
circumference = distance around the circle
In other words, if you had a curved fence around the circle, then the circumference is the perimeter of that circle (telling you how much fencing you need, assuming there's no waste)
The formula for the circumference is C = pi*d where d is the diameter. In this case, 24 ft is the diameter because this segment goes from one point on the circle to another, and this line goes through the center.
The circumference of this full circle is...
C = pi*d
C = pi*24 ... replace d with 24
C = 24pi
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Now we don't want the whole distance around the circle. We only want a small fraction of it. Specifically from A to C along the shortest route (this is called minor arc AC). The angle measure of arc AC is 120 degrees. Why? This is because 180 - x = 180 - 60 = 120, the x = 60 refers to the measure of minor arc BC. The two arc measures combine to get 180 degrees.
Using the fact that minor arc AC is 120 degrees, this means the distance along the arc AC is 120/360 = 1/3 of the entire circumference. Note how I divided 120 over 360 because there are 360 degrees in a full circle
So...
distance along minor arc AC = (1/3)*(circumference)
distance along minor arc AC = (1/3)*(24pi)
distance along minor arc AC = 8pi