I call it similarity!

Geometry Level 3

Find the value of \(x\), if \( ABCD\) is a square. A line passes through \(B\) intersects \(CD\) produced at \(E\), the side \(AD\) at \(F\) and the diagonal \(AC\) at \(G\). And \(BG =3\), and \(GF =1\).

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