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Radical axis passes through curvilinear touch point

Source: Sharygin Geometry Olympiad, Final Round 2016, Problem 8 grade 9

August 4, 2016
geometrygeometry proposedHi

Problem Statement

The diagonals of a cyclic quadrilateral meet at point MM. A circle ω\omega touches segments MAMA and MDMD at points P,QP,Q respectively and touches the circumcircle of ABCDABCD at point XX. Prove that XX lies on the radical axis of circles ACQACQ and BDPBDP.
(Proposed by Ivan Frolov)
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