The square which is made in a circle such that all four vertices of a square touches circle is called Circumscribed square.

Square in Circle

By Pythagoras theorem in triangle BOC

s2    =  r2 + r2

s = √2r

Areas In terms of radius ‘r’In terms of side ‘s’
Area of square ABCD with side ‘s’ 2 r2 s2
Area of circle with radius ‘r’ ∏ r2 ∏ s2 /2

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