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 $\angle BGA$ ?