Cool Geometry!

Geometry Level 5

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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