In the figure, \(ABCD\) is a trapezoid with \(BC \parallel AD\), \(AB = CD\), \(BE \parallel CG\), and angle \(AEB = 90º\). Point \(M\) is the midpoint of side \(BC\). Point \(F\), not shown, is a vertex on triangle \(EFG\) such that \(EF = FG\). Is point \(F\) inside the trapezoid?

(1) \(BE = EG\)

(2) \(FG\parallel CD\)

[spoiler]OA=E[/spoiler]

Source: Magoosh