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Concyclicity on some quadrilateral from isosceles triangle

Source: ISL 2018 G2

July 17, 2019
IMO Shortlistgeometrygeometry solvedsymmetryAngle ChasingMiquel point

Problem Statement

Let ABCABC be a triangle with AB=ACAB=AC, and let MM be the midpoint of BCBC. Let PP be a point such that PB<PCPB<PC and PAPA is parallel to BCBC. Let XX and YY be points on the lines PBPB and PCPC, respectively, so that BB lies on the segment PXPX, CC lies on the segment PYPY, and ∠PXM=∠PYM\angle PXM=\angle PYM. Prove that the quadrilateral APXYAPXY is cyclic.
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