Question

Each side of an equilateral triangle is $a$ cm. Find out the ratio of areas of the circumcircle and the incircle of the triangle:

• A. 1 : 2
• B. 2 : 1
• C. 4 : 1
• D. 1 : 4

Answer 1

The correct option is C 4 : 1

Circum radius $R=\frac{a}{\sqrt{3}}$
In radius $r=\frac{a}{2\sqrt{3}}$
$\frac{Areaofcircumcircle}{Areaofincirlce}=\frac{\frac{\pi a^2}{3}}{\frac{\pi a^2}{12}}$
$\Rightarrow \frac{12}{3}=\frac{4}{1}$
Hence, option 'C' is correct.