Problem 12 (2018 AMC 10B)
AMC 10BHard
From module Medians and the Centroid
Problem
Line segment AB is a diameter of a circle with center O and radius 6. Point C, not equal to A or B, lies on the circle. As point C moves around the circle, the centroid of triangle ABC traces out a closed curve. To the nearest positive integer, what is the area of the region bounded by this curve?