Question

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

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.  MathematicsSecondary School Mathematics XStandard X

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