SOLUTION: a square is inscribed in a circle. if the diagonal of the square measures 6 in. what is the exact area of the circle?

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Question 328504: a square is inscribed in a circle. if the diagonal of the square measures 6 in. what is the exact area of the circle?
Found 2 solutions by galactus, solver91311:
Answer by galactus(183) About Me  (Show Source):
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Let a circle side be x.
Since the sides are all the same length, we have
x%5E2%2Bx%5E2=36
2x%5E2=36
x%5E2=18
x=3%2Asqrt%282%29
Since this is a side length, the circle's radius is half that.
The area of a circle is %28pi%29%2Ar%5E2 with r=3%2Asqrt%282%29%2F2
area of circle: %28pi%29%2A%283%2Asqrt%282%29%2F2%29%5E2=9%2A%28pi%29%2F2
As an added bonus, the area of the square is 18.
the ratio of the square area to the circle area is 18%2F%289%2A%28pi%29%2F2%29=4%2F%28pi%29
This is true in general.

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


If a square is inscribed in a circle, then the diagonal of the square is a diameter of the circle. Half of the diameter is the radius. Square the radius and multiply times . Leave it in terms of for the exact answer.

John