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prove that <BGE <= < AED / 2

Source: 2015 Sharygin Geometry Olympiad Correspondence Round P3

August 2, 2018
geometryisoscelessquare

Problem Statement

The side ADAD of a square ABCDABCD is the base of an obtuse-angled isosceles triangle AEDAED with vertex EE lying inside the square. Let AFAF be a diameter of the circumcircle of this triangle, and GG be a point on CDCD such that CG=DFCG = DF. Prove that angle BGEBGE is less than half of angle AEDAED.
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