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Math Help - Help Geometry Problem

  1. #1
    Newbie
    Joined
    May 2007
    Posts
    6

    Help Geometry Problem

    The inner circle is inscribed in the square, and the square is inscribed in the outer circe. If the area of the outer circle is 256(pi) square millimeters, find the area of the inner circle.

    (here there is a picture of a large circle, that holds a square whose corners touch the circle, and a smaller circle that fits inside the square)

    there are 4 multiple choice answeres..
    basically i already know that the answer is 128(pi) mm squared..but i have NO idea why

    so PLEAAASEE just give me the steps.. thank you so much!
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  2. #2
    MHF Contributor
    Joined
    Apr 2005
    Posts
    1,631
    Let r = radius of inner circle.

    The radius R of the outer circle is a diagonal of any of the 4 squares that make up the one big square.
    And this, by Pythagorean theorem is
    R^2 = r^2 +r^2
    R^2 = 2r^2 -----------------***


    Big circle,
    Area = pi(R)^2 = 256pi
    pi(2r^2) = 256pi
    2r^2 = 256
    r^2 = 256/2
    r^2 = 128

    Small circle,
    Area = pi(r^2) = pi(128) = 128pi sq.mm -------------answer.
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