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.
+36916 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 rs^2 / pi rl^2 (s = amall l = large)
rs 2 / rl2 = (sqrt2/4)^2 / (1/2)^2 = 2/16 / 1/4 = 8/16 = 1/2 = ratio: area small / area large
