$\begin{aligned} & \text { In } \triangle A B C, \\ & =\frac{\Delta}{s-a} \cdot \frac{\Delta}{s-b}+\frac{\Delta}{s-b} \cdot \frac{r_1 r_2+r_2 r_3+r_3 r_1}{s-c}+\frac{\Delta}{s-c} \cdot \frac{\Delta}{s-a} \\ & =\frac{\Delta^2}{(s-a)(s-b)(s-c)}[s-c+s-a+s-b]\end{aligned}$
$\begin{aligned} & =\frac{\Delta^2 3 s-(a+b+c)}{(s-a)(s-b)(s-c)} \quad(\because 2 s=a+b+c) \\ & =\frac{\Delta^2(3 s-2 s)}{(s-a)(s-b)(s-c)}=\frac{\Delta^2 \cdot s}{\left(\frac{\Delta^2}{s}\right)} \\ & \quad\left[\because \frac{\Delta^2}{s}=(s-a)(s-b)(s-c)\right] \\ & =\frac{s^2 \cdot \Delta^2}{\Delta^2}=\frac{\Delta^2}{\left(\frac{\Delta}{s}\right)^2}=\frac{\Delta^2}{r^2} \quad\left[\because r=\frac{\Delta}{s}\right]\end{aligned}$