IGO 2020 I4

Triangle $ABC$ is given. An arbitrary circle with center $J$ , passing through $B$ and $C$ , intersects the sides $AC$ and $AB$ at $E$ and $F$ , respectively. Let $X$ be a point such that triangle $FXB$ is similar to triangle $EJC$ (with the same order) and the points $X$ and $C$ lie on the same side of the line $AB$ . Similarly, let $Y$ be a point such that triangle $EYC$ is similar to triangle $FJB$ (with the same order) and the points $Y$ and $B$ lie on the same side of the line $AC$ . Prove that the line $XY$ passes through the orthocenter of the triangle $ABC$ .

Proposed by Nguyen Van Linh - Vietnam