Question

Construct the circumcircle and incircle of an equilateral $△ABC$ with side $6cm$ and centre $O$. Find the ratio of radii of circumcircle and incircle.

Answer 1

Let $a$ be the side length of $△ABC$ with centre $O$. The radius of the incircle is $r=\frac{\sqrt{3}a}{6}=\sqrt{3}cm$.The radius of the circumcircle is given as $R=\frac{\sqrt{3}a}{3}=2\sqrt{3}cm$.

$\therefore \frac{R}{r}=2$ is the required answer.