RMO 2011 Problem 1

Let $ABC$ be a triangle. Let $D, E, F$ be points respectively on the segments $BC, CA, AB$ such that $AD, BE, CF$ concur at the point $K$ . Suppose $\frac{BD}{DC} = \frac {BF}{FA}$ and $\angle ADB = \angle AFC$ . Prove that $\angle ABE = \angle CAD$ .