SHARYGIN 2022 Problem 93

A medial line parallel to the side $AC$ of triangle $ABC$ meets its circumcircle at points at $X$ and $Y$ . Let $I$ be the incenter of triangle $ABC$ and $D$ be the midpoint of arc $AC$ not containing $B$ .A point $L$ lie on segment $DI$ in such a way that $DL= BI/2$ . Prove that $\angle IXL = \angle IYL$ .