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Math Help - 4 circles

  1. #1
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    4 circles

    Ready to run around in circles?

    Four circles radius 4, centers (4,9), (28,9), (16,4), (16,18),
    are each tangent to one side of an isosceles trapezoid.
    All four tangent points are situated at middle of each side.

    Gimme the trapezoid's side lengths (the one with height=6).

    If you wish, you could try the possible trapezoid(s) that contain
    the four circles.
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  2. #2
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    Quote Originally Posted by Wilmer View Post
    Ready to run around in circles?

    Four circles radius 4, centers (4,9), (28,9), (16,4), (16,18),
    are each tangent to one side of an isosceles trapezoid.
    All four tangent points are situated at middle of each side.

    Gimme the trapezoid's side lengths (the one with height=6).

    If you wish, you could try the possible trapezoid(s) that contain
    the four circles.
    h = 6, side dim = 6.93
    Attached Thumbnails Attached Thumbnails 4 circles-trapcircle0001.jpg  
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  3. #3
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    Quote Originally Posted by aidan View Post
    h = 6, side dim = 6.93
    Agree. Your C2 diagram: equal sides = 12 / sqrt(3) ; your 6.93.
    Other 2 sides: 24 - 6sqrt(3) and 24 -2 sqrt(3).

    NICE diagrams. Thanks.
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  4. #4
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    General case

    Four circles radius 4, centers (4,9), (28,9), (16,4), (16,18) : original givens

    Four circles radius r, centers (r,w), (3r+2u,w), (2r+u,r), (2r+u,3r+2v) : as a general case

    General case where all 4 circles are outside the trapezoid
    ===========================================

    4 circles radius r, centers (r,w), (3r+2u,w), (2r+u,r), (2r+u,3r+2v)

    longer parallel side = 2(2r + u - b)
    shorter parallel side = 2[2(r - a) + u + b]
    the two equal sides = 2SQRT[(a - b)^2 + v^2]

    where
    a = r + sqrt(r^2 - k) where k = 4r(r + v - w) + (v - w)^2
    b = [v(2r + v - w) + a(r - a)] / (r - a)

    Anybody disagree?!
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