The above shows a square that has both a circumscribed circle and a circle inscribed inside of it. Find the ratio of areas between the smaller circle versus the larger circle.

Guest Jul 27, 2020

#1**+1 **

Let's make the DIAMETER of the larger circle 1

the diagonal of the square is thus 1

using pythag theorem the sides of the square are then sqrt2 / 2

sqrt2/2 is also the DIAMETER of the smaller circle

pi r_{s}^2 / pi r_{l}^2 (s = amall l = large)

r_{s }^{2} / r_{l}^{2 }= (sqrt2/4)^2 / (1/2)^2 = 2/16 / 1/4 = 8/16 = 1/2 = ratio: area small / area large

ElectricPavlov Jul 27, 2020