Question

In $△ABC,\angle C=\frac{\pi }{2},a=4,b=3$, then the value of $\frac{R}{r}$ is equal to?

• A. $\frac{9}{2}$
• B. $\frac{17}{4}$
• C. $\frac{10}{3}$
• D. $\frac{5}{2}$

Answer 1

The correct option is D $\frac{5}{2}$

$c^2=a^2+b^2=9+16=25⟹c=5$

$2R=\frac{c}{\sin C}⟹2R=c=5$

$r=(s-c)\tan \frac{C}{2}⟹r=\frac{a+b+c}{2}-c⟹2r=a+b-c=2$

$\therefore \frac{R}{r}=\frac{5}{2}$