Question 1
Let $\Gamma$ be the circumcircle of triangle $ABC$, and let $D$ lie on side $BC$. The tangent to $\Gamma$ at $A$ meets the line through $D$ parallel to $BA$ at $E$. The segment $CE$ meets $\Gamma$ again at $F$. Suppose $B,D,F,E$ are concyclic. Prove that $AC,BF,DE$ are concurrent.
