Question

In any $\Delta$ABC, $4(\frac{s}{a}-1)(\frac{s}{b}-1)(\frac{s}{c}-1)$ is equal to

• A. r/R
• B. 2r/R
• C. 3r/R
• D. 4r/R

Answer 1

The correct option is A

r/R

We have, $4(\frac{s}{a}-1)(\frac{s}{b}-1)(\frac{s}{c}-1)=4.\frac{(s-a)(s-b)(s-c)}{abc}=4.\frac{s(s-a)(s-b)(s-c)}{s.abc}=4.\frac{{\Delta }^2}{s.abc}=\frac{4\Delta }{abc}.\frac{\Delta }{s}=\frac{r}{R}$