CMOQR 2013 Problem 2

In triangle $ABC$ , $\angle A = 90^\circ$ and $\angle C = 70^\circ$ . $F$ is point on $AB$ such that $\angle ACF = 30^\circ$ , and $E$ is a point on $CA$ such that $\angle CF E = 20^\circ$ . Prove that $BE$ bisects $\angle B$ .