# Isosceles Circumcircle

**Geometry**Level 4

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 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 \(\angle BGA \)?