Question 56
Let $ABC$ be an acute triangle, and $AX$, $AY$ two isogonal lines. Also, suppose that $K$, $S$ are the feet of perpendiculars from $B$ to $AX$, $AY$, and $T$, $L$ are the feet of perpendiculars from $C$ to $AX$, $AY$ respectively. Prove that $KL$ and $ST$ intersect on $BC$.