Area Ratio, Circle and Square 2

A circle and a square have the same area. What is the ratio of the area of a square inscribed in the circle to the area of a circle inscribed in the square? (Draw nice pictures.)


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pir2 = s2r2 = s2 / pi
A1 = Asquare = half the product of the diagonals = ½(2r · 2r) = 2r2
A2 = Acircle = pi(s/2)2 = pis2 / 4
A1 / A2 = (2r2) / (pis2 / 4)
= (2s2/pi) / (pis2 / 4)
= 2s2/pi · 4/pis2
= 8/pi2

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