2018 AMC 12B Problem 8

Line segment \overline{AB} is a diameter of a circle with AB = 24. Point C, not equal to A or B, lies on the circle. As point C moves around the circle, the centroid (center of mass) of \triangle ABC traces out a closed curve missing two points. To the nearest positive integer, what is the area of the region bounded by this curve?

\textbf{(A) } 25 \qquad \textbf{(B) } 38 \qquad \textbf{(C) } 50 \qquad \textbf{(D) } 63 \qquad \textbf{(E) } 75

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.