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Circumcircle of half of an isosceles triangle

Source: Junior Turkish Mathematical Olympiad 2011 P2

July 2, 2012
geometrycircumcircleanalytic geometrygraphing linesslopepower of a pointradical axis

Problem Statement

Let ABCABC be a triangle with ∣AB∣=∣AC∣|AB|=|AC|. DD is the midpoint of [BC][BC]. EE is the foot of the altitude from DD to ACAC. BEBE cuts the circumcircle of triangle ABDABD at BB and FF. DEDE and AFAF meet at GG. Prove that ∣DG∣=∣GE∣|DG|=|GE|
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