Question 156
Let $ABC$ be a triangle and $D$, $E$ be points on segments $AB$, $AC$ respectively, such that $DE \parallel BC$. Let the circumcircle of $ABC$ meet the circumcircles of $BDE$ and $CDE$ again at $K$, $L$ respectively. Let $T$ be the intersection of the lines $BK$ and $CL$. Prove that $TA$ is tangent to the circumcircle of $ABC$.