On a circle with diameter $AB$, lie points $C$ and $D$. $XY$ is the diameter passing through the midpoint $K$ of the chord $CD$. Point $M$ is the projection of point $X$ onto line $AC$, and point $N$ is the projection of point $Y$ on line $BD$. Prove that points $M, N$ and $K$ are collinear. (A. Zaslavsky)