Question 122
Let $ABC$ a triangle, $\Gamma$ his circumscribed circle and $\omega$ the circle of the same center as $\Gamma$ and tangent to the line $(BC)$. The tangents in the circle $\omega$ via $A$ cut $(BC)$ at one point $X$ towards $B$ and at a point $Y$ towards $C$. The tangent to the circle $\Gamma$ in $B$ and the parallel to the line $(AC)$ via $X$ intersect at a point $S$ and the tangent to the circle $\Gamma$ in $C$ and the parallel to the line $(AB)$ via $Y$ intersect at a point $T$. Show that the line $(ST)$ is tangent to the circle $\Gamma$.
