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drawing parallels to diagonals of trapezoid, passing through intersection

Source: 2011 Sharygin Geometry Olympiad Correspondence Round P10

April 2, 2019
geometrytrapezoiddiagonalsparallelIntersection diagonals

Problem Statement

The diagonals of trapezoid ABCDABCD meet at point OO. Point MM of lateral side CDCD and points P,QP, Q of bases BCBC and ADAD are such that segments MPMP and MQMQ are parallel to the diagonals of the trapezoid. Prove that line PQPQ passes through point OO.
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