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What is the ratio of the incircle area and circumcircle area of a square?

Option:
A. 1:1
B. 1:2
C. 1:4
D. 2:1
Answer: B . 1:2

Justification:

Side of the Square is L.

So, radius of the incircle r = L/2.

The radius of the circumcirlce R = Sq. root of (r^2 + r^2) = Sq. root of (2) * r

=> R^2 = 2 * r^2

 

The area of the incircle a = Pi * r * r

The area of the circumcircle A = Pi * R * R = Pi * 2 * r^2 = 2 * Pi * r * r = 2 * a

 

The Ratio of the area of incircle to the circumcirclr = a / (2 *a) = 1 / 2 => 1:2

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