Geometry Problem 373: Square, Inscribed Circle, Diagonal, Perpendicular, Angle

The figure shows a circle 1 inscribed in a
square ABCD of area S. Points E and F are the tangency point. G is the
intersection point of BD and circle 1 and EH is perpendicular to FG.
Prove that the measure of angle EAH is 22.5 degrees. .