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 reason for your answer.

Answer 1

Correct answer is False

Solution: 

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,

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.