EGMO 2023 | Problem 2 - 17 April 2023

Problem 2.
We are given an acute triangle $ABC$ . Let $D$ be the point on its circumcircle such that $AD$ is a diameter. Suppose that points $K$ and $L$ lie on segments $AB$ and $AC$ , respectively, and that $DK$ and $DL$ are tangent to circle $AKL$ .
Show that line $KL$ passes through the orthocenter of triangle $ABC$ .