IZhO 2023 Problem 2

The tangent at $C$ to $\Omega$ , the circumcircle of scalene triangle $ABC$ intersects $AB$ at $D$ . Through point $D$ , a line is drawn that intersects segments $AC$ and $BC$ at $K$ and $L$ respectively. On the segment $AB$ points $M$ and $N$ are marked such that $AC \parallel NL$ and $BC \parallel KM$ . Lines $NL$ and $KM$ intersect at point $P$ lying inside the triangle $ABC$ . Let $\omega$ be the circumcircle of $MNP$ . Suppose $CP$ intersects $\omega$ again at $Q$ . Show that $DQ$ is tangent to $\omega$ .