Let $G$ be the intersection point of lines $BC$ and $FA$. Two circles lie outside regular hexagon $ABCDEF$. The first is tangent to $\overline{AB}$. The second is tangent to a line $L$ parallel to $\overline{AB}$ and $\overline{DE}$, such that the distance from $G$ to $L$ is 5 times the distance from $G$ to $\overline{AB}$. Both circles are tangent to lines $BC$ and $FA$. What is the ratio of the area of the second circle to that of the first circle?