# Isosceles Circumcircle

Geometry Level 3

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

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