Question

in a figure a square is inscribed in a circle of diameter d and another square circumscribing the circle. find the ratio of area of outer square to the area of inner square

Answer 1

Of square inscribed in circle ,

Diagonal of square = Diameter of circle = D ( say)

By Pythagoras theorem,

diagonal^2 = side^2 + side^2

D^2 = 2 s^2

s = √ D^2/2

area = √D^2/2 × √D^2/2

=D^2/2

For square circumscribing the circle ,

Side of square = diameter of circle = D(say)

Area = D×D = D^2

so ratio : D^2 / (D^2/2)

=2:1