Question 95
Points $L$ and $H$ are marked on the sides $AB$ of an acute-angled triangle $ABC$ so that $CL$ is a bisector and $CH$ is an altitude. Let $P$, $Q$ be the feet of the perpendiculars from $L$ to $AC$ and $BC$ respectively.
Prove that $AP \cdot BH = BQ \cdot AH$. (I. Gorodnin)
Prove that $AP \cdot BH = BQ \cdot AH$. (I. Gorodnin)