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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