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prove that points are concyclic

Source: Kyiv mathematical festival 2021

May 8, 2021
Kyiv mathematical festivalgeometry

Problem Statement

Let ADAD be the altitude, AEAE be the median, and OO be the circumcenter of a triangle ABC.ABC. Points XX and YY are selected inside the triangle such that ∠BAX=∠CAY,\angle BAX=\angle CAY, OX⊥AX,OX\perp AX, and OY⊥AY.OY\perp AY. Prove that points D,E,X,YD,E,X,Y are concyclic. (M. Kurskiy)
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