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Thread: Find a point M

  1. #1
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    Exclamation Find a point M

    The side lengths of a triangle ABC are $AB=9, BC=\sqrt{39}, CA=\sqrt{201}$. Find a point M on the circle (C;3) such that the sum $MA+MB$ is the maximum.
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  2. #2
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    Re: Find a point M

    There appears to be an error in the question
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  3. #3
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    Re: Find a point M

    I am sure this question which, i asked ,is true
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  4. #4
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    Re: Find a point M

    Hello, leezangqe!

    This is a strange problem . . .


    The side lengths of \Delta ABC are AB=9,\;BC=\sqrt{39},\;CA=\sqrt{201}.

    Find a point M on the circle (C;3) such that the sum M\!A+M\!B is a maximum.

    I assumed that (C;3) means: center at C, radius 3.

    I found that the graph looks somewhat like this:

    Code:
      |                             * * *
      |                         *           *  M
      |                       *               o
      |                      *                 *
      |
      |                     *         C    3    *
      |                     *         ♥ - - - - *
      |                     *     *  *          *
      |                       *     *
      |          ___      *  *     * __        *
      |         √201  *       *   * √39       *
      |           *             **          *
      |       *                 *   * * *
      |   *                   B*
    A ♥  *  *  *  *  *  *  *  ♥ - - - - - - - - - - -
    (0,0)                   (9,0)
    I found that C has approximate coordinates: (13.5,\,4.33)

    For the maximum sum of M\!A + M\!B,
    . . M must be in the upper-right quadrant of the circle.

    Am I right so far?
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  5. #5
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    Re: Find a point M

    Thank you, but i want a solution logic and present it
    your solution is Expected.
    I thank you very much
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  6. #6
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    Re: Find a point M

    Who can help me?
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  7. #7
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    Re: Find a point M

    So far you have shown no interest in the problem at all yourself so why should any one else be interested? Soroban asked about exactly what your question was and you refused to answer.
    Thanks from leezangqe
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  8. #8
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    Re: Find a point M

    Hi leezangqe,

    I can't give an analytic or geometric solution to the problem, but here's a numeric solution:

    Find a point M-mhfgeometry3a.png
    Thanks from leezangqe
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  9. #9
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    Re: Find a point M

    I think it's (C,\sqrt{3}) not (C,3)
    I have seen it before
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  10. #10
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    Re: Find a point M

    What do you do with this problem if (C,\sqrt{3}) ?
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  11. #11
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    Re: Find a point M

    i haven't solve it yet.
    It is in a magazine
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