jmc

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 $△ABC$ traces out a closed curve missing two points. To the nearest positive integer, what is the area of the region bounded by this curve? $\text{(A)}\text{indent}25\text{(B)}\text{indent}32\text{(C)}\text{indent}50\text{(D)}\text{indent}63\text{(E)}\text{indent}75$