Question 21
The largest angle of triangle $ABC$ is located at its vertex $C$. Let $\rho$ be the circle with centre $A$ and radius $AC$, and let $\sigma$ be the circle with centre $B$ and radius $BC$. The circle $\sigma$ intersects the circumcircle of the triangle $ABC$ and the circle $\rho$ at points $D$ and $F$, respectively ($D \neq C$, $F \neq C$). Prove that $A$, $D$ and $F$ are collinear.