Question 161
In an acute triangle $ABC$ points $D$ and $E$ are on the sides $[AC]$ and $[AB]$, respectively, such that $BD$ and $CE$ are angle bisectors. Projections of $D$ onto $BC$ and $BA$ are $P$ and $Q$, respectively, projections of $E$ onto $CA$ and $CB$ are $R$ and $S$, respectively. Let $X$ be intersection of $AP$ and $CQ$, $Y$ be the intersection of $AS$ and $BR$, $Z$ be the intersection of $BX$ and $CY$. Show that $AZ \perp BC$.