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AD and BC meet MN at P and Q

Source: Baltic Way 2005

December 28, 2010
geometryparallelogramrhombustrigonometrygeometry proposed

Problem Statement

Let ABCDABCD be a convex quadrilateral such that BC=ADBC=AD. Let MM and NN be the midpoints of ABAB and CDCD, respectively. The lines ADAD and BCBC meet the line MNMN at PP and QQ, respectively. Prove that CQ=DPCQ=DP.
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