Question

In figure, a square is inscribed in a circle of diameter d and another square is circumscribing the circle. Is the area of the outer square four times the area of the inner square? Give reasons for your answer.

Answer 1

Given diameter of circle is d.

∴ Diagonal of inner square = Diameter of circle = d

Let side of inner square EFGH be x.

∴ In right angled ΔEFG,

EG² = EF² + FG²   ...[By Pythagoras theorem]

⇒ d² = x² + x²

⇒ d² = 2x²

⇒ x² = `"d"^2/2`

∴ Area of inner square EFGH = (Side)²

= x²

= `"d"^2/2`

But side of the outer square ABCD = Diameter of circle = d

∴ Area of outer square = d²

Hence, area of outer square is not equal to four times the area of the inner square.