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Part of 2003 Indonesia MO

Problems(1)

An intersection of the lines connecting opposite midpoints

Source:

8/5/2011
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.
geometryparallelogramgeometry unsolved