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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.

 

 Jul 27, 2020
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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

 Jul 27, 2020

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