TUYMAADA 2024 J6

Extension of angle bisector $BL$ of the triangle $ABC$ (where $AB < BC$ ) meets its circumcircle at $N$ . Let $M$ be the midpoint of $BL$ . Isosceles triangle $BDC$ with base $BC$ and angle equal to $ABC$ at $D$ is constructed outside the triangle $ABC$ . Prove that $CM \perp DN$ . Proposed by А. Mardanov