A quad
Source: Indian RMO 2004 Problem 5
February 28, 2006
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Problem Statement
Let ABCD be a quadrilateral; X and Y be the midpoints of AC and BD respectively and lines through X and Y respectively parallel to BD, AC meet in O. Let P,Q,R,S be the midpoints of AB, BC, CD, DA respectively. Prove that
(A) APOS and APXS have the same area
(B) APOS, BQOP, CROQ, DSOR have the same area.