SOLUTION: A rectangle is placed inside a circle of radius r so the center of the rectangle and the center of the circle coincide, and the corners of the rectangle are on the circle. Express

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Question 259789: A rectangle is placed inside a circle of radius r so the center of the rectangle and the center of the circle coincide, and the corners of the rectangle are on the circle. Express the area of the rectangle as a function of the length x of one of its sides.
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Consider one quadrant:
x^2 + y^2 = r^2
y = sqrt(r^2 - x^2)
Area = x*y
Area = x*sqrt(r^2 - x^2)
Total area = 4xsqrt(r^2 - x^2)
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To use x as one side, not 1/2 of one side:
Area = 2x*sqrt(4r^2 - x^2)