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Thread: Triangle problem to solve - please help!!!

  1. #1
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    Unhappy Triangle problem to solve - please help!!!

    Iv'e been given a problem as part of my undergrad degree and I'm really struggling. Here's the question:

    Consider for an arbitrary triangle the possibility of cutting it with a straight line such that its perimeter is halved. Can this be done if we specify the direction of the line?
    What about if we specify a point to pass through?
    Are there any points with more than one such line through them? If so, is this true of all points?
    Is it possible to have exactly two such lines through any point?

    I know it's a long problem, but any help with even a small part of it would be really really appreciated. Thanks in advance!!
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  2. #2
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    Re: Triangle problem to solve - please help!!!

    A line will intersect a triangle at 0, 1, or 2 points. If the line divides the circumference in half, then if you one of the points, there can be only one point that will equally divide the circumference. Yes, you can start with only a direction for the line. Use continuity and the Intermediate Value Theorem to prove it along with the fact that the sum of the length of any two sides is greater than the length of the third.
    Thanks from topsquark
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  3. #3
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    Re: Triangle problem to solve - please help!!!

    Thankyou! How can you apply the IVT on triangles?
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