SOLUTION: Square ABCD is inscribed in a circle. Find the ratio of the area of the square to the area of the circle.
Example of a Diagram: https://imgur.com/a/0SgrQoX
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-> SOLUTION: Square ABCD is inscribed in a circle. Find the ratio of the area of the square to the area of the circle.
Example of a Diagram: https://imgur.com/a/0SgrQoX
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Question 1149200: Square ABCD is inscribed in a circle. Find the ratio of the area of the square to the area of the circle.
Example of a Diagram: https://imgur.com/a/0SgrQoX Answer by greenestamps(13206) (Show Source):
Consider the diagonals of the square. Each is a diameter of the circle. Let r be the radius of the circle.
The diagonals of the square divide the square into four 45-45-90 right triangles. The side length of the square (the hypotenuse of one of those right triangles) is sqrt(2) times the length of the radius of the circle.
