A obtuse \(\Delta ABC\) is made with one of the angles equal to \(120^\circ\).

\(\Delta DEF\) is made by joining the feet of the angle bisectors of \(\Delta ABC\).

Two sides of \(\Delta DEF\) (in no particular order) are each \(100\) units in length.

The third side is \(x\) units. Find magnitude of \(x^{2}\)?

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