# 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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