Question 27
In the adjoining figure triangle $ABC$ is inscribed in a circle. Point $D$ lies on $\overset{\frown}{AC}$ with $\overset{\frown}{DC}=30^\circ,$ and point $G$ lies on $\overset{\frown}{BA}$ with $\overset{\frown}{BG}\gt\overset{\frown}{GA}.$ Side $AB$ and side $AC$ each have length equal to the length of chord $DG,$ and $\angle CAB=30^\circ.$ Chord $DG$ intersects sides $AC$ and $AB$ at $E$ and $F,$ respectively. The ratio of the area of $\triangle AFE$ to the area of $\triangle ABC$ is
