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.
Hello, leezangqe!
This is a strange problem . . .
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:
I found that $\displaystyle C$ has approximate coordinates: $\displaystyle (13.5,\,4.33)$Code:| * * * | * * M | * o | * * | | * C 3 * | * ♥ - - - - * | * * * * | * * | ___ * * * __ * | √201 * * * √39 * | * ** * | * * * * * | * B* A ♥ * * * * * * * ♥ - - - - - - - - - - - (0,0) (9,0)
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?