Is it enough?

Geometry Level 5

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 \(S_1\).

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