Question 50
The excircle $\omega_{B}$ of triangle $ABC$ opposite $B$ touches side $AC$, rays $BA$ and $BC$ at $B_{1}$, $C_{1}$ and $A_{1}$, respectively. Point $D$ lies on major arc $\widetilde{A_{1}C_{1}}$ of $\omega_{B}$. Rays $DA_{1}$ and $C_{1}B_{1}$ meet at $E$. Lines $AB_{1}$ and $BE$ meet at $F$. Prove that line $FD$ is tangent to $\omega_{B}$ (at $D$).