Find the ratio of the areas of the incircle and circumcircle of a square.
Correct Answer: Option B
Let the side of the square be x. Then, its diagonal = \(\sqrt{2x^2}=\sqrt{2x}\)
Radius of incircle = \(\frac x2\)
Radius of circum circle= \(\sqrt2\times\frac x2=\frac x{\sqrt2}\)
Required ratio = \(\frac{\mathrm{πx}^2}4:\frac{\displaystyle\mathrm{πx}^2}{\displaystyle2}=\frac14:\frac12=1:2\)
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