CAUCASUS 2022 Problem 7

Point $P$ is chosen on the leg $CB$ of right triangle $ABC$ ( $\angle ACB = 90^\circ$ ). The line $AP$ intersects the circumcircle of $ABC$ at point $Q$ . Let $L$ be the midpoint of $PB$ . Prove that $QL$ is tangent to a fixed circle independent of the choice of point $P$ .