A geometry problem by Brilliant Member

Geometry Level pending

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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