BALTIC-WAY 2007 Problem 12

Let $M$ be a point on the arc $AB$ of the circumcircle of the triangle $ABC$ which does not contain $C$ . Suppose that the projections of $M$ onto the lines $AB$ and $BC$ lie on the sides themselves, not on their extensions. Denote these projections by $X$ and $Y$ , respectively. Let $K$ and $N$ be the midpoints of $AC$ and $XY$ , respectively. Prove that $\angle MNK=90^{\circ}$ .