SHARYGIN 2020 Problem 16

Cevians $AP$ and $AQ$ of a triangle $ABC$ are symmetric with respect to its bisector. Let $X$ , $Y$ be the projections of $B$ to $AP$ and $AQ$ respectively, and $N$ , $M$ be the projections of $C$ to $AP$ and $AQ$ respectively. Prove that $XM$ and $NY$ meet on $BC$ .