OIM 2022 Problem 5

Let $ABC$ be an acute triangle with circumcircle $\Gamma$ . Let $P$ and $Q$ be points in the half plane defined by $BC$ containing $A$ , such that $BP$ and $CQ$ are tangents to $\Gamma$ and $PB = BC = CQ$ . Let $K$ and $L$ be points on the external bisector of the angle $\angle CAB$ , such that $BK = BA, CL = CA$ . Let $M$ be the intersection point of the lines $PK$ and $QL$ . Prove that $MK=ML$ .