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Math Help - Is it possible to find out the length of X in this diagram?

  1. #1
    dgu
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    Question Is it possible to find out the length of X in this diagram?

    Is it possible to find out the length of X in this diagram?

    Is it possible to find out the length of X in this diagram?-circle-math-question.jpg

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  2. #2
    MHF Contributor
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    Re: Is it possible to find out the length of X in this diagram?

    I assume these are squares inscribed in circles. Let the circle radius be r. From trigonometry or Pythagorean theorem it follows that half of the square side is r * sqrt(2) / 2, so x = r(1 - sqrt(2) / 2). We also have 4r - 2x = 100, from where r and then x can be found.
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  3. #3
    MHF Contributor
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    Re: Is it possible to find out the length of X in this diagram?

    ...or, the given 100 being h, general case:

    x = h(1 - f) / 2 where f = 2SQRT(2) / [2 + SQRT(2)]

    As Mr Makarov says, squares inside the circles are assumed.
    r = radius, k = squares side length.
    You have:
    h = 2k + 2x : x = (h - 2k) / 2
    and:
    r - x = k/2 : x = (2r - k) / 2
    So h - 2k = 2r - k
    And since r = k / SQRT(2), you can easily get x in terms of h.

    Good nuff?
    Last edited by Wilmer; May 15th 2012 at 10:31 AM.
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