Problem 13 (2018 AMC 12B)
AMC 12BHard
From module Medians and the Centroid
Problem
Square ABCD has side length 1. Point P lies inside the square so that AP = 2BP = 2CP. The centroids of triangles ABP, BCP, CDP, and DAP are the vertices of a convex quadrilateral. What is the area of that quadrilateral?