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Convex quadrilateral and midpoints [RMO2-2011, India]

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December 31, 2011
geometryanalytic geometryprojective geometry

Problem Statement

Let ABCDABCD be a convex quadrilateral. Let E,F,G,HE,F,G,H be the midpoints of AB,BC,CD,DAAB,BC,CD,DA respectively. If AC,BD,EG,FHAC,BD,EG,FH concur at a point O,O, prove that ABCDABCD is a parallelogram.
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