Question

in the figure, a square is inscribed in a circle of diameter d and another square is circumscribing the circle. find the ratio of the area of the innere square

Answer 1

diameter will be the hypotenuse of the small square and a parallel line for a side in the large square.

so in small square,(a -- side)

(a)2 + (a)2 = (d)2

2(a)2=(d)2

side a= d/ root 2

in large square ,(A----side)

A= d

side A= d

now to find ratio =large square area/small square area

= (d)2/2/(d)2

=1/2

thus the ration is 2:1 and the larger circle is not 4 times the small one.

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