If I know the coordinates of a right angle triangle how can I find the distance between the centroid and the incircle?

Question

I have points $A(6,0)$, $B(6,8)$ and $C(0,8)$

Answer 1

Draw $\Delta ABC$.

$AB=8$, $AC=10$ and $BC=6$.

Thus, $r=\frac{6+8-10}{2}=2$ and the incenter $I(6-2,8-2)$ or $I(4,6)$.

In another hand the centroid $M\left(\frac{6+6+0}{3},\frac{0+8+8}{3}\right)$ or $M\left(4,\frac{16}{3}\right)$.

Thus, $IM=6-\frac{16}{3}=\frac{2}{3}$