Question 66
Let $ABC$ be an isosceles triangle with $AB = AC$. Let $D$ and $E$ be the midpoints of segments $AB$ and $AC$, respectively. Suppose that there exists a point $F$ on ray $\overrightarrow{DE}$ outside of $ABC$ such that triangle $BFA$ is similar to triangle $ABC$. Compute $\frac{AB}{BC}$.
