Question

The ratio of areas of incircle and circumcircle of a square is

Answer 1

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The ratio of areas of incircle and circumcircle of a square is 1:2.

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Answer 2

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$\large\sf\color{navy}{Let \: the \: side \: of \: the \: square \: be \: x. \: Then, its \: diagonal =  \sqrt{2x}^{2} = \sqrt{2x} }$

$\large\sf\color{navy}Radius \: of \: incircle = \frac{x}{2}$

$\large\sf\color{navy}Radius \: of \: circum \: circle= \sqrt{2} \times \frac{x}{2} = \frac{x}{ \sqrt{2} }$

$\large\sf\bold\color{navy}Required \: ratio = \frac{\pi {x}^{2} }{4} : \frac{\pi {x}^{2} }{2}$

$\huge\implies\color{navy} \frac{1}{4} : \frac{1}{2}= {\fbox{\color{gold}{1:2}}}$

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