A difficult problem, learn to give directions, thank you.

The crossing point D is that DE is perpendicular to AB, and E is vertical foot.

From BD is the bisector of the angle, we know that CD = de, BC = be.

(The distance between the points on the bisector of the angle is equal to both sides of the angle) (or the triangular BCD is equal to the triangular bed)

In the right triangle ADE, the angle A=45 degrees.

Get AE=DE, AE=CD.

AB=AE+BE=CD+BC (equivalent substitution)