Question

If the sides of a triangle are in ratio $3:7:8$, the ratio of the circumradius to the inradius

i.e. $R:r$ is equal to?

• A. $2:7$
• B. $7:2$
• C. $3:7$
• D. $7:3$

Answer 1

The correct option is B $7:2$

Let the sides be $3k,7k,8k$

$s=\frac{a+b+c}{2}$

Also, $\Delta =\sqrt{s(s-a)(s-b)(s-c)}$

And finally $R=\frac{abc}{4\Delta }$

Using teh above formlae, we get

$s=9k$

Now

$\Delta =\sqrt{9k\times 6k\times 2k\times k}=6\sqrt{3}{k}^2$

$R=\frac{3k\times 7k\times 8k}{4\times 6\sqrt{3}{k}^2}$

$=\frac{7k}{\sqrt{3}}$

$r=\frac{6\sqrt{3}{k}^2}{9k}=\frac{2k}{\sqrt{3}}$

$\therefore \frac{R}{r}=\frac{7}{2}$