2018 AMC 10B Problem 12

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 \qquad

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