IR-TST 2014 Problem 1

suppose that $O$ is the circumcenter of acute triangle $ABC$ . we have circle with center $O$ that is tangent too $BC$ that named $w$ suppose that $X$ and $Y$ are the points of intersection of the tangent from $A$ to $w$ with line $BC$ ( $X$ and $B$ are in the same side of $AO$ ) $T$ is the intersection of the line tangent to circumcirle of $ABC$ in $B$ and the line from $X$ parallel to $AC$ . $S$ is the intersection of the line tangent to circumcirle of $ABC$ in $C$ and the line from $Y$ parallel to $AB$ . prove that $ST$ is tangent $ABC$ .