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Question

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


Solution

First let ABCD be the square inscribed in the circle.

Let diameter of circle be 2r.

Since square ABCD is inscribed in the circle , diagonal AC and BD will be equal to the diameter (2r)

therefore, BD = 2r

In triangle BCD inside square ABCD ,

BC2 + CD2 = BD2

BC2 + BC2 = (2r)2 ( BD = 2r , BC = CD)

2BC2 = 4r2

BC2 = 2r2

Ratio of Areas of circle and the square = area of circle / area of square = pie r2 / BC2 = 22 / 7 * r2 / 2r2 (BC2=2r2)

= 22 / 7 / 2 

= 11 / 7


Mathematics

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