Christmas Contest - Individual Round - Problem 20

Let ABC be a triangle such that \angle ACB = 90^\circ. The point D lies inside triangle ABC and on the circle with centre B that passes through C. The point E lies on the side AB such that \angle DAE = \angle BDE. The circle with centre A that passes through C meets the line through D and E at the point F, where E lies between D and F. If \angle ABF = 20^\circ, find \angle AFE.