Question

A square has been inscribed in a circle.. what is the ratio of the length of a side of the square to the radius of the circle

Answer 1

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Let , the radius be r of a circle

let , the side of square be x

ATQ,

see, the figure above

x²+x²=(2r)² {•°• pythogorous- theorem}

2x²=4r²

x²=2r²

x=√(2r²)

x=r√2

So, the ratio between side of square and radius of circle:-

x/r=r√2/r=√2/1

x:r = √2:1

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