Simple Similarity

Geometry Level 3

\(ABCD\) is a parallelogram. The point \(E\) is in the segment \(BC\), and \(F\) is a point in the line \(DC\) such that \(AF\) pass through the point \(E\) and intersect the segment \(BD\) in the point \(G\). If \(AG=6\) and \(GE=4\). How long is \(EF\)?

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