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Question

A square is inscribed in a circle. Find the ratio of the areas of the circle and the square.

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Solution

First, inscribed meaning inside of something.

first radius of the circle is r
then diagonal of the circle is equal to the diagonal of the square, means 2r

now length(l) of one side of the square is,
l\sqrt{2} = 2r \\ l = 2r \div \sqrt{2} \\ l = r2 \sqrt{2} \div 2
now area of the square should be,
{(r2 \sqrt{2} \div 2 )}^{2} \\ {r}^{2} 8 \div 4 \\ {r}^{2} 2
now you know the area of a circle which is
\pi {r}^{2}
now ratio of them is,
r²2:πr²
2:π is the answer.


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