Problem

Source: Central American Olympiad 2000, problem 3

Tags: geometry, parallelogram, trigonometry, analytic geometry, graphing lines, slope, complex numbers



Let ABCDE be a convex pentagon. If P, Q, R and S are the respective centroids of the triangles ABE, BCE, CDE and DAE, show that PQRS is a parallelogram and its area is 2/9 of that of ABCD.