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