SILK-ROAD 2018 Problem 1

In an acute-angled triangle $ABC$ on the sides $AB$ , $BC$ , $AC$ the points $H$ , $L$ , $K$ so that $CH \perp AB$ , $HL \parallel AC$ , $HK \parallel BC$ . Let $P$ and $Q$ feet of altitudes of a triangle $HBL$ , drawn from the vertices $H$ and $B$ respectively. Prove that the feet of the altitudes of the triangle $AKH$ , drawn from the vertices $A$ and $H$ lie on the line $PQ$ .