Isosceles Circumcircle

Geometry Level 3

Triangle ABCABC is an isosceles triangle with AB=BC\overline{AB}=\overline{BC} and ABC=123 \angle ABC = 123 ^ \circ . Point DD is the midpoint of AC\overline{AC}, point EE is the foot of the perpendicular from DD to BC,\overline{BC}, and point FF is the midpoint of DE\overline{DE}. The intersection point of AE\overline{AE} and BF\overline{BF} is GG. What is the measure (in degrees) of BGA\angle BGA ?

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