# Find a point M

• Jan 26th 2013, 02:53 AM
leezangqe
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.
• Jan 26th 2013, 08:28 AM
ibdutt
Re: Find a point M
There appears to be an error in the question
• Jan 26th 2013, 03:17 PM
leezangqe
Re: Find a point M
I am sure this question which, i asked ,is true
• Jan 26th 2013, 05:53 PM
Soroban
Re: Find a point M
Hello, leezangqe!

This is a strange problem . . .

Quote:

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

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

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

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 $\displaystyle C$ has approximate coordinates: $\displaystyle (13.5,\,4.33)$

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

Am I right so far?
• Jan 26th 2013, 07:26 PM
leezangqe
Re: Find a point M
Thank you, but i want a solution logic and present it
I thank you very much
• Jan 27th 2013, 05:28 AM
leezangqe
Re: Find a point M
Who can help me?
• Jan 27th 2013, 06:22 AM
HallsofIvy
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.
• Jan 27th 2013, 11:08 AM
johng
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:

Attachment 26725
• Mar 4th 2013, 01:50 AM
coriander
Re: Find a point M
I think it's (C,\sqrt{3}) not (C,3)
I have seen it before
• Mar 4th 2013, 06:45 AM
leezangqe
Re: Find a point M
What do you do with this problem if (C,\sqrt{3}) ?
• Mar 4th 2013, 07:33 AM
coriander
Re: Find a point M
i haven't solve it yet.
It is in a magazine