TH-TMO 2019 Problem 8

Let $ABC$ be a triangle such that $AB\ne AC$ and $\omega$ be the circumcircle of this triangle. Let $I$ be the center of the inscribed circle of $ABC$ which touches $BC$ at $D$ . Let the circle with diameter $AI$ meets $\omega$ again at $K$ . If the line $AI$ intersects $\omega$ again at $M$ , show that $K, D, M$ are collinear.