OSN 2015 Problem 3

Given an acute triangle $ABC$ . $\Gamma _{B}$ is a circle that passes through $AB$ , tangent to $AC$ at $A$ and centered at $O_{B}$ . Define $\Gamma_C$ and $O_C$ the same way. Let the altitudes of $\triangle ABC$ from $B$ and $C$ meets the circumcircle of $\triangle ABC$ at $X$ and $Y$ , respectively. Prove that $A$ , the midpoint of $XY$ and the midpoint of $O_{B}O_{C}$ is collinear.