Triangle in Verse!

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 $x$ .