Triangle in Verse!

Geometry Level pending

In a Triangle $$ABC$$, we have $$({II_1})^2$$ + $$({{I_2}{I_3}})^2$$ $$=$$ $$xR^2$$, where $$I$$ denotes incentre. $$I_1$$, $$I_2$$ and $$I_3$$ denote centres of the circles escribed to the sides $$BC$$, $$CA$$ and $$AB$$ respectively, and $$R$$ be the radius of the circumcircle of triangle $$ABC$$. Find $$x$$.

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