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.

Options

• True

• False

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]

⇒ `d^2 = x^2 + x^2`

⇒ `d^2 = 2x^2`

⇒ `x^2 = d^2/2`

∴ Area of inner square EFGH = (Side)² = `x^2 = d^2/2`

But side of the outer square ABCS = 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.