SMO 2010 Problem 1

Let $CD$ be a chord of a circle $\Gamma_1$ and $AB$ a diameter of $\Gamma_1$ perpendicular to $CD$ at $N$ with $AN > NB$ . A circle $\Gamma_2$ centered at $C$ with radius $CN$ intersects $\Gamma_1$ at points $P$ and $Q$ . The line $PQ$ intersects $CD$ at $M$ and $AC$ at $K$ ; and the extension of $NK$ meets $\Gamma_2$ at $L$ . Prove that $PQ$ is perpendicular to $AL$