TIMO - 2018 - Grade 8 - Heat Round - Paper 4 Question 16

In the figure, $AB=AC$. Point $D$ lies on $AB$, $E$ lies on the extension of $AC$, and $DE$ intersects $BC$ at $F$. Given $\frac{FC}{BF}=\frac18$ and $\frac{AB}{AE}=\frac34$, find $\frac{DF}{FE}$.