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Square inscribed in a circle

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An Indian sand painter begins his picture with a circle of dark sand. He then inscribes a square with a side length of 1 foot inside the circle. What is the area of the circle?

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Assuming that the circle touches all four corners of the square then the diagonal of ...

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This is a word problem regarding a square inscribed in a circle.

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Infinite Geometric Series: Square Inscribed in Circle Radius

A square is inscribed in a circle of radius 100. The area of that circle which lies outside of the square is shaded. Another circle is inscribed in the square, and then a second square is inscribed in that second circle. The area of the second circle which lies outside of the second square is shaded. This process is continued to infinity. What is the sum of all of the shaded areas? How do I find this?
First Area w/ following:
Radius of circle - 100
Side of - __________
Area of - ______________
Area of ________________
Difference ______________
Second Area - ?
Radius of circle - ?
Side of - ?
Area of - ?
Area of - ?
Difference - ?
Third area - ? (as above) & Fourth area - ?
Each new area is ___________of the previous area.

_____________Sum of areas (shaded areas).

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