IGO 2020 I3

In acute-angled triangle $ABC$ ( $AC > AB$ ), point $H$ is the orthocenter and point $M$ is the midpoint of the segment $BC$ . The median $AM$ intersects the circumcircle of triangle $ABC$ at $X$ . The line $CH$ intersects the perpendicular bisector of $BC$ at $E$ and the circumcircle of the triangle $ABC$ again at $F$ . Point $J$ lies on circle $\omega$ , passing through $X, E,$ and $F$ , such that $BCHJ$ is a trapezoid ( $CB \parallel HJ$ ). Prove that $JB$ and $EM$ meet on $\omega$ .

Proposed by Alireza Dadgarnia