Line segment \overline{A B} is a diameter of a circle with A B=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 A B C traces out a closed curve missing two points. To the nearest positive integer, what is the area of the region bounded by this curve?
Answer Choices
A. 25
B. 38
C. 50
D. 63
E. 75