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  1. #1
    Bronze Lounger
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    Perimeter of quadrilateral

    I'm attaching the image and explanation of the problem.
    It's not really a puzzle or trick. I know the answer but am unsure how to PROVE that BC = 4.
    Attached Images Attached Images

  2. #2
    Super Moderator BATcher's Avatar
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    I can see what you mean! Stating the obvious, you have to show that the lines AB and EC are parallel, as are the lines EB and DC. "They just are" doesn't really cut the mustard...
    BATcher

    "The trouble with quotes on the internet is that you can never know if they are genuine."
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  3. #3
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    AE and BC are parallel because both triangles ABE and ECD are equilateral (all sides are radii of the circle) so all the angles in the two triangles are 60 degress.

    So angle DAB is the same as DEC.

    So also angle BEC is 60 degress (to make 180) so triangle BEC is also equilateral.
    Regards
    John



  4. #4
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    There you have it! Thanks.
    Last edited by kweaver; 2011-09-24 at 09:42. Reason: ah ha experience.

  5. #5
    Gold Lounger Maudibe's Avatar
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    I know the answer but am unsure how to PROVE that BC = 4.
    Here is a different logic to solve the problem:

    circle2.png

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