Given square ABCD with E on AB, F on BC, G on CD, H on DA, AE=BF=CG=DH. Segments AF, BG, CH, DE dissect the square into 4 triangles, 4 trapezoids and a central square.

If the circle inscribed in the square has the same radius as the incircles of the triangles, find AE/AB.

Note: exact solution is the solution to a cubic equation.