MathNet 2017-part-04 — 176 problems (EN–VI) Question 15

Let $\omega$ be the circumcircle of triangle $ABC$ and let $AD$ and $BE$ be altitudes. The line $DE$ intersects the circle $\omega$ at points $P$ and $Q$, in the order $P$, $E$, $D$, $Q$ on the line. Let the bisectors of angles $APQ$ and $BQP$ intersect the circle $\omega$ at points $K$ and $L$, respectively. Prove that the line $KL$ is perpendicular to the bisector of angle $ACB$.
(Proposed by B. Ulziinasan)