SOLUTION: Square ABCD is inscribed in a circle. Find the ratio of the area of the square to the area of the circle.

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Question 1205152: Square ABCD is inscribed in a circle. Find the ratio of the area of the square to the area of the circle.
Answer by MathLover1(20850) About Me  (Show Source):
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We know that if a circle circumscribes a square, then the diameter of the circle is equal to the diagonal of the square.
d+=+2r
we also know that the area of square is
A=%281%2F2%29d%5E2
substituting d=2r, area is
A=%281%2F2%29%282r%29%5E2
A=%281%2F2%294r%5E2
A=2r%5E2 => the area of square expressed in terms of radius

the area of the circle
A%5Bc%5D=pi%2Ar%5E2

the ratio of the area of the square to the area of the circle
A%2FA%5Bc%5D=%282r%5E2%29%2F%28pi%2Ar%5E2%29=2%2Fpi