The vertices of a triangle are the points $A (- 36, 7), B (20, 7)$ and $\mathrm{C} (0, - 8).$ If G and I be the

centroid and incentre of the triangle, then $GI$ is equal to 

The co-ordinates of G are $\left(\frac{-16}{3},2\right)$ For in centre we have to calculate the lengths of sides $a,b,c$which are $25, 39, 56$ respectively. Hence, the incentre is

$\left(\frac{\sum a{x}_i}{a+b+c},\frac{\sum a{y}_j}{a+b+c}\right)=(-1,0)$

$\therefore GI={\left[{\left(-1+\frac{16}{3}\right)}^2+(0-2{)}^2\right]}^{1/2}=\frac{1}{3}\sqrt{205}\Rightarrow \left(\mathrm{c}\right)$