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

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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. .
 

Square, Inscribed Circle, Angles
 

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