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Feet of angle bisectors and two vertices are Concyclic!!

Source: Sharygin 2022 P16

March 4, 2022
geometryangle bisector

Problem Statement

Let ABCDABCD be a cyclic quadrilateral, E=AC∩BDE = AC \cap BD, F=AD∩BCF = AD \cap BC. The bisectors of angles AFBAFB and AEBAEB meet CDCD at points X,YX, Y . Prove that A,B,X,YA, B, X, Y are concyclic.
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