Question

Sides of $△ABC$ are equal. What is the ratio of circum-radius and in-radius of the triangle?

• A. $\frac{1}{4}$
• B. $\frac{1}{2}$
• C. $2$
• D. $4$

Answer 1

Answer: (C)

$2$

$△ABC$ is equilateral triangle.

$\therefore \angle A=\angle B=\angle C={60}^{\circ }$

$r=4R\sin \frac{A}{2}\sin \frac{C}{2}\sin \frac{C}{2}$

$⟹\frac{r}{R}=4\times \frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}=\frac{1}{2}$

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