Answer :

For a square inscribing the circle,

Diagonal of the square = diameter of the circle

Let the radius of the circle be r

⇒ Diagonal of the circle = 2r

We know that the diagonal of the square = √2 side

⇒√2 side = 2r

⇒Side of the inscribed circle = √2r

Area of the inscribed square = side× side

⇒ Area of the inscribed circle = 2r^{2}

For a square circumscribing the circle,

Side of the square = diameter of the circle

⇒ Side of the circumscribed circle = 2r

Area of the circumscribed square = side× side

⇒Area of the circumscribed circle = 4r^{2}

Ratio of area of two square circumscribe and inscribe by a circle

⇒ Ratio = 2:1

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