Question

A square is inscribed in a circle of diameter d and another square is circumscribing the circle. Find the ratio of the outer square to the area of the inner 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.

Answer 2

Answer:

1 : 2

Step-by-step explanation:

Let a be the side of the square.

The side of the square will be the diameter of the inscribed circle.

Radius of inscribed circle = a/2

Area of inscribed circle = π(a/2)2 = 1/4 a2π

The diagonal of the square will be the diameter of the circumscribed circle.

Radius of circumscribed circle = √2a/2

Area of circumscribed circle = π(√2a/2)2 = 1/2 a2π

The ratio of the area is 1 : 2

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