Question 18
Let $ABC$ be a triangle with circumcircle $\Gamma$, $D$ a point on $(AB)$ and $E$ a point on $(AC)$ such that $(DE)$ and $(BC)$ are parallel. The circumcircle of $ABC$ meets the circumcircle of $BDE$ a second time at $K$ and the circumcircle of $CDE$ a second time at $L$. Let $T$ be the intersection point of $(BK)$ and $(CL)$. Show that $(TA)$ is tangent to the circle $\Gamma$.