MathNet 2014 Question 58

Let $ABCD$ be a square and consider the points $K \in (AB)$, $L \in (BC)$, and $M \in (CD)$ such that $KLM$ is a right isosceles triangle, with the right angle at $L$. Prove that the lines $AL$ and $DK$ are perpendicular to each other.

Bogdan Enescu