Question 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?