Question 52
Let $\triangle ABC$ be a triangle with $AB \lt AC$ inscribed into a circle $c$. The tangent of $c$ at the point $C$ meets the parallel from $B$ to $AC$ at the point $D$. The tangent of $c$ at the point $B$ meets the parallel from $C$ to $AB$ at the point $E$ and the tangent of $c$ at the point $C$ at the point $L$. Suppose that the circumcircle $c_1$ of the triangle $BDC$ meets $AC$ at the point $T$ and the circumcircle $c_2$ of the triangle $BEC$ meets $AB$ at the point $S$. Prove that the lines $ST, BC, AL$ are concurrent.