The ratio of the area of the incircle and cir | vedclass

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(C) Let the side of the square be $x$.The radius of the incircle $(r)$ is half the side of the square: $r = \frac{x}{2}$.The area of the incircle is $

Vedclass · Accepted Answer

$1:2$

Vedclass · Answer

(C) Let the side of the square be $x$.The radius of the incircle $(r)$ is half the side of the square: $r = \frac{x}{2}$.The area of the incircle is $A_1 = \pi r^2 = \pi (\frac{x}{2})^2 = \frac{\pi x^2}{4}$.The diagonal of the square is $\sqrt{2}x$. The radius of the circumcircle $(R)$ is half the diagonal: $R = \frac{\sqrt{2}x}{2} = \frac{x}{\sqrt{2}}$.The area of the circumcircle is $A_2 = \pi R^2 = \pi (\frac{x}{\sqrt{2}})^2 = \frac{\pi x^2}{2}$.The ratio of the area of the incircle to the circumcircle is $\frac{A_1}{A_2} = \frac{\pi x^2 / 4}{\pi x^2 / 2} = \frac{2}{4} = 1:2$.

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

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