In parallelogram \(ABCD\) shown above, point \(E\) lies on diagonal \(AC\). Line \(BE\) extended meets \(CD\) at \(F\) and \(AD\) at \(G\). Given that \(AD=10,DG=4\) and \(BG=11,\) find the length of \(EF\) correct to four decimal places.

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