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center of parallelogram

Source: I.F.Sharygin contest 2009 - Correspondence round - Problem 21

May 31, 2009
geometryparallelogramgeometry proposed

Problem Statement

The opposite sidelines of quadrilateral ABCD ABCD intersect at points P P and Q Q. Two lines passing through these points meet the side of ABCD ABCD in four points which are the vertices of a parallelogram. Prove that the center of this parallelogram lies on the line passing through the midpoints of diagonals of ABCD ABCD.
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