Question

Find the ratio of the areas of the incircle and circumcircle of a square.

• A. 1:1
• B. 1:2
• C. 1:3
• D. 1:4

Answer 1

The correct option is B

1:2

Let the side of the square be $x$.

Then, its diagonal = $\sqrt{2}$x

Radius of incircle = $\frac{x}{2}$

AO is the radius of cicum circle but it is also hypotnuse of an isoscles triangle with side $\frac{x}{2}$.

So,radius of circum circle= $\sqrt{2}$ x $\frac{x}{2}$ = $\frac{x}{\sqrt{2}}$

Required ratio = $\frac{\pi x^2}{4}$ : $\frac{\pi x^2}{2}$ = $\frac{1}{4}$ : $\frac{1}{2}$ = 1 : 2