Problem

Source: Kyiv mathematical festival 2021

Tags: Kyiv mathematical festival, geometry



Let $AD$ be the altitude, $AE$ be the median, and $O$ be the circumcenter of a triangle $ABC.$ Points $X$ and $Y$ are selected inside the triangle such that $\angle BAX=\angle CAY,$ $OX\perp AX,$ and $OY\perp AY.$ Prove that points $D,E,X,Y$ are concyclic. (M. Kurskiy)