Question 94
Let $ABC$ be an isosceles and obtuse triangle in $A$. Let $\Gamma$ be the center circle $B$ passing through $A$, and $\Omega$ the center circle $C$ passing through $A$. Let $D$ be the intersection point of the circle $\Gamma$ with the segment $[BC]$, $E$ the second intersection point on the line $(AD)$ with the circle $\Omega$, and $F$ the point of intersection of the line $(BC)$ with the circle $\Omega$ which is not on the $[BC]$ segment. Show that the triangle $DFE$ is isosceles in $F$. 