SOLUTION: A square is inscribed in a circle. The same square is also circumscribed about a smaller circle. What is the ratio of the area of the larger circle to the area of the smaller circl

Algebra ->  Circles -> SOLUTION: A square is inscribed in a circle. The same square is also circumscribed about a smaller circle. What is the ratio of the area of the larger circle to the area of the smaller circl      Log On


   

Question 1117179: A square is inscribed in a circle. The same square is also circumscribed about a smaller circle. What is the ratio of the area of the larger circle to the area of the smaller circle?

Answer by math_helper(2461) About Me  (Show Source):
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Let s = length of each side of the square
The diameter d%5B1%5D of the small circle is then +s, +d%5B1%5D+=+s+
The diameter of the large circle is equal to the diagonal length of the square: +d%5B2%5D+=+s%2Asqrt%282%29+

+A%5B2%5D+=+pi%2A%28d%5B2%5D%2F2%29%5E2+=+pi%2A%28s%5E2%2A2%29%2F4+
+A%5B1%5D+=+pi%2A%28d%5B1%5D%2F2%29%5E2+=+pi%2A%28s%5E2%29%2F4%29+
+A%5B2%5D%2F+A%5B1%5D+=+highlight%28++2++%29 —> or equivalently, the ratio of large to small is 2:1