If $I_1,I_2,I_3$  are excentres of the triangle with vertices $\left(1,\sqrt{3}\right),\left(0,0\right)$  and $\left(2,0\right)$ , then the orthocentre of $\Delta I_1{I}_2{I}_3$  is

Which is Equilateral triangle

The triangle is equilateral then the orthocentre of $\Delta I_1{I}_2{I}_3=$ centroid of $\Delta ABC=$ $=\left(\frac{1+0+2}{3},\frac{\sqrt{3}}{3}\right)=\left(1,\frac{1}{\sqrt{3}}\right)$