Is it enough?

The figure shows a circle $\mathfrak{C}$ , which is inscribed in a square $ABCD$ of area $S$ . Points $E, F, G$ and $H$ are the tangency point. $M$ is the point of intersection of $DF$ and $AG$ and $N$ is the point of intersection of $DF$ and circle $\mathfrak{C}$ . If $S_1$ is the area of triangle $GMN$ , Then find the ratio $S$ to $S_1$ .