Question

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

Answer 1

Answer:

Let the side of the square be x. Then it's

diagonal =

$\sqrt{2x { }^{2} } = \sqrt{2x}$

Radius of circle =x/2

Radius of circumcircle

$\sqrt{2} \times x \div 2 = x \div \sqrt{2}$

required ratio = πx2/4 : πx2/2

= 1/4 : 1/2

= 1 : 2

1 : 2 is the correct answer