Question

In a $△ABC,a:b:c=4:6:8$. The ratio of the radius of the incircle to that of the circumcircle is

• A. $\frac{5}{64}$
• B. $\frac{64}{5}$
• C. $\frac{5}{32}$
• D. $\frac{32}{5}$

Answer 1

The correct option is A $\frac{5}{64}$

$\frac{a}{4}=\frac{b}{6}=\frac{c}{8}=k$

$\frac{r}{R}=\frac{\Delta }{s}\times \frac{4\Delta }{abc}$

$=\frac{4{\Delta }^2}{sabc}=\frac{4(s-a)(s-b)(s-c)}{abc}$

$=\frac{4(s-a)(s-b)(s-c)}{abc}=\frac{5\cdot 3\cdot 1k^3}{4\cdot 6\cdot 8k^3}=\frac{5}{64}$