Question

If $r_1,r_2,r_3$ represent the exradii and r represents the inradius then, $\frac{1}{r_1}+\frac{1}{r_2}+\frac{1}{r_3}-\frac{1}{r}$ = 0

• A. True
• B. False

Answer 1

The correct option is A True

$r_1=\frac{\Delta }{s-a}andr=\frac{\Delta }{s}\frac{1}{r_1}+\frac{1}{r_2}+\frac{1}{r_3}-\frac{1}{r}=\frac{s-a}{\Delta }+\frac{s-b}{\Delta }+\frac{s-c}{\Delta }-\frac{s}{\Delta }=\frac{3s-(a+b+c)}{\Delta }-\frac{s}{\Delta }=\frac{3s-\left(2s\right)-s}{\Delta }=\frac{3s-3s}{\Delta }=0$
$\therefore$ Given statement is true