MathDB

1

Part of 2020 Czech-Austrian-Polish-Slovak Match

Problems(1)

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

Source: 2020 Czech-Polish-Slovak Match p1

10/8/2020
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)
geometryparallelogramcircumcircleComputer problems