RU-SPB 2009 Problem 107

Points $Y,X$ lies on $AB,BC$ of $\triangle ABC$ and $X,Y,A,C$ are concyclic. $AX$ and $CY$ intersect in $O$ . Points $M,N$ are midpoints of $AC$ and $XY$ . Prove, that $BO$ is tangent to circumcircle of $\triangle MON$