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Area of a parallelogram

Source: Central American Olympiad 2000, problem 3

August 8, 2007
geometryparallelogramtrigonometryanalytic geometrygraphing linesslopecomplex numbers

Problem Statement

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