homework problem "perp"

Given points A, B, and D not on line AB, construct the circle with center B and radius BD, and the circle with center A and radius AD. These circles intersect at D and another point E.
Prove that the line DE is perpendicular to line AB.

You can use axioms, the theorem that a triangle is isosceles if and only if the base angles are congruent, theorems about supplementary angles, vertical angles, and the triangle congruence theorems (SAS, ASA, AAS, and SSS). Don't (directly) use theorems about medians and altitudes in special triangles.

If you prefer, you can download the Geogebra file for this construction, or here is a static image.

Created with GeoGebra