Geometry Problem 595: Triangle, Equal Angles, Isogonal Lines, Similarity

The figure shows a triangle ABC with the angle ABD equal to angle CBE. If AB = c, BC = a, AD = d₁, DC = d₂, AE = e₁, and EC = e₂, prove that .
BD and BE are called isogonal conjugates, since they form the same angle with the bisector of angle ABC.