MathNet 2008-part-05 — 164 problems (EN–VI) Question 20

Let $ABC$ be a right triangle with $\angle A = 90^{\circ}$. Let $D$ be the midpoint of $AB$ and let $E$ be a point on segment $AC$ such that $AD = AE$. Let $BE$ meet $CD$ at $F$. If $\angle BFC = 135^{\circ}$, determine $BC / AB$.