Question 90
Let $ABCD$ be a parallelogram. Perpendiculars $AX$ and $AY$ are drawn from $A$ to $BC$ and $CD$, respectively (so $X$ lies on $BC$ and $Y$ lies on $CD$). Parallel lines $l$ and $d$ are drawn such that $l$ is perpendicular to $XY$. Line $l$ intersects $AB$ and $BC$ at $K$ and $L$ respectively, and line $d$ intersects $AD$ and $DC$ at $P$ and $Q$ respectively. Furthermore, line $l$ bisects segment $AX$, and line $d$ bisects segment $AY$. Prove that the circumcircles of $\triangle DPQ$ and $\triangle BKL$ are tangent to each other.