BALKAN-SL 2008 G7

In the non-isosceles triangle $ABC$ consider the points $X$ on $[AB]$ and $Y$ on $[AC]$ such that $[BX]=[CY]$ , $M$ and $N$ are the midpoints of the segments $[BC]$ , respectively $[XY]$ , and the straight lines $XY$ and $BC$ meet in $K$ . Prove that the circumcircle of triangle $KMN$ contains a point, different from $M$ , which is independent of the position of the points $X$ and $Y$ .