Question

If $r_1,r_2,r_3$ are the ex-radii of a traingle
then the value of $\frac{1}{r_1}+\frac{1}{r_2}+\frac{1}{r_3}$ equals?

• A. $1$
• B. $-1$
• C. $r$
• D. $\frac{1}{r}$

Answer 1

The correct option is D $\frac{1}{r}$

$\frac{1}{r_1}+\frac{1}{r_2}+\frac{1}{r_3}=\frac{s-a}{△}+\frac{s-b}{△}+\frac{s-c}{△}$
Where, $s$ is the semi perimeter, $a,b\&c$ are the sides of the triangle and $△$ is the area of triangle.
$\Rightarrow \frac{1}{r_1}+\frac{1}{r_2}+\frac{1}{r_3}=\frac{3s-2s}{△}=\frac{s}{△}=\frac{1}{r}$
Ans: D