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

False

Explanation

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 `DeltaEFG`,
`EG^(2) = EF^(2) + FG^(2)` [by Pythagoras theorem]
`rArr d^(2) = x^(2)+ x^(2)`
`rArr d^(2) = 2x^(2) rArr 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 = `d^(2)`
Hence, area of outer square is not equal to four times the area of the inner square.