Team Selection Test for JBMO 2023

Let $ABC$ be an acute angled triangle and $K,L$ be points on $AC,BC$ respectively such that $\angle AKB=\angle ALB$. Let $P$ be the intersection of $AL,BK$ and $Q$ be the midpoint of segment $KL$. Let $T,S$ be the intersection $AL,BK$ with the circumcircle of $ABC$, respectively. Prove that $TK,SL,PQ$ are concurrent.