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square and tangent line

Source: Moroccan Olympiad 2005 Problem 1

March 12, 2005
geometry

Problem Statement

In a square ABCDABCD let FF be the midpoint of [CD]\left[ CD\right] and let EE be a point on [AB]\left[ AB\right] such that AE>EBAE>EB . the parallel with (DE)\left( DE\right) passing by FF meets the segment [BC]\left[ BC\right] at HH. Prove that the line (EH)\left( EH\right) is tangent to the circle circumscribed with ABCDABCD
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