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collinear wanted, ABCD parallllogram tangents of circumcircle of MAD,MBC

Source: 2020 Czech-Polish-Slovak Match p1

October 8, 2020
geometryparallelogramcircumcircleComputer problems

Problem Statement

Let ABCDABCD be a parallelogram whose diagonals meet at PP. Denote by MM the midpoint of ABAB. Let QQ be a point such that QAQA is tangent to the circumcircle of MADMAD and QBQB is tangent to the circumcircle of MBCMBC. Prove that points Q,M,PQ,M,P are collinear.
(Patrik Bak, Slovakia)
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