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collinear with the parallelogram's center (Singapore Junior 2012)

Source:

July 11, 2019
geometrycollinearparallelogram

Problem Statement

Let OO be the centre of a parallelogram ABCDABCD and PP be any point in the plane. Let M,NM, N be the midpoints of AP,BPAP, BP, respectively and QQ be the intersection of MCMC and NDND. Prove that O,PO, P and QQ are collinear.
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