Question 15
Let a triangle $ABC$ be given. A circle $k$ passes through $A$, meets the sides $\overline{AB}$ and $\overline{AC}$ again at the points $D$ and $E$ respectively, and meets the side $\overline{BC}$ at the points $F$ and $G$, where $F$ lies between $B$ and $G$. The tangent at $F$ to the circle through $B$, $D$ and $F$ and the tangent at $G$ to the circle through $C$, $E$ and $G$ meet at a point $T$. We assume that $A \neq T$. Prove that the lines $AT$ and $BC$ are parallel.
