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.
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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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