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    Infinite Geometric Series: Square Inscribed in Circle Radius

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    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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    https://brainmass.com/math/algebraic-geometry/infinite-geometric-series-square-inscribed-circle-radius-40652

    Solution Summary

    The solution finds the sum of all the shaded areas of the square.

    $2.49

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