If I₁,I₂, I₃ are excentres of the triangle with vertices (0,0), (5,12),(16,12) then the orthocentre of ${\mathrm{\Delta I}}_1{\mathrm{I}}_2{\mathrm{I}}_3$ is

A =(0,0),B=(5, 12),Q=(16, 12)$\Rightarrow$ a = 11,b=20,c = 13
Orthocentre of ${\mathrm{\Delta I}}_1{\mathrm{I}}_2{\mathrm{I}}_3=$ Incentre of $\mathrm{△}\mathrm{ABC}$
$=\left(\frac{11\left(0\right)+20\left(5\right)+13\left(16\right)}{11+20+13},\frac{11\left(0\right)+20\left(12\right)+13\left(12\right)}{11+20+13}\right)=(7,9)$