Question

In a triangle $ABC,$ if $a:b:c=3:7:8$, then $R:r$ is equal to:

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

Answer 1

Answer: (B)

$7:2$

$R=\frac{abc}{4△}andr=\frac{△}{s}$

$\frac{R}{r}=\frac{abc}{4△}\cdot \frac{s}{△}=\frac{abc}{4(s-a)(s-b)(s-c)}$

$a:b:c=3:7:8$

$\frac{a}{3}=\frac{b}{7}=\frac{c}{8}=k$

$\therefore s=\frac{3k+7k+8k}{2}=9k$

$\therefore \frac{R}{r}=\frac{3k\times 7k\times 8k}{4\left(6k\right)\left(2k\right)\left(k\right)}\Rightarrow \frac{7}{2}$

Hence, $7:2$ is the correct answer.