Thread: 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.

There appears to be an error in the question

I am sure this question which, i asked ,is true

Hello, leezangqe!

This is a strange problem . . .

The side lengths of are

Find a point on the circle such that the sum is a maximum.

I assumed that means: center at , radius

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 has approximate coordinates:

For the maximum sum of
. . must be in the upper-right quadrant of the circle.

Am I right so far?

Thank you, but i want a solution logic and present it
your solution is Expected.
I thank you very much

Who can help me?

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.

Hi leezangqe,

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

I think it's (C,\sqrt{3}) not (C,3)
I have seen it before

What do you do with this problem if (C,\sqrt{3}) ?

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