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An intersection of the lines connecting opposite midpoints

Source:

August 5, 2011
geometryparallelogramgeometry unsolved

Problem Statement

Let ABCDABCD be a quadrilateral, and P,Q,R,SP,Q,R,S are the midpoints of AB,BC,CD,DAAB, BC, CD, DA respectively. Let OO be the intersection between PRPR and QSQS. Prove that PO=ORPO = OR and QO=OSQO = OS.
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