Question

In the figure below, the small square is inscribed in the circle., which is inscribed in the large square. What is the ratio of the area of the large square to the area of the small square?

Answer 1

from this we can say the length of large square is 2r
length of small square is 2x

note that triangle is a 45-45-90 right triangle
thus x = r/sqrt2

Area large square = 4r^2
Area of small square = 4x^2 = 4r^2/2 = 2r^2

ratio = 2/1