Question 124
Let $F$ be a point on the side $AC$ of a triangle $ABC$. A line through $F$ and parallel to $AB$ intersects side $BC$ at $D$. Similarly, a line through $F$ and parallel to $BC$ intersects side $AB$ at $E$. Assume that the side $AC$ is tangent to the circumcircle of $EDF$. If $AB : BC = k$, then prove that $AF : FC = k^2$.