Hello, Blasnmt23!
I used a simpler approach . . .
Code:

o  ....♥ B
 ....*::::::*
....*::::::::::::*
....*:::::::::::::::::*
A ♥:::::::::::::::::::::::* o
*::::::::::::::::::*
o *:::::::::::::* o
o *::::::::* o
o  *::::* o
o  ♥
        o   C       

Point has coordinates
Point has coordinates
Point has coordinates
The area of is given by: .
We have: .
. . . . . . . .
Maximize: .
. . . . . . .
The coordinates of point are: .
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
Fascinating!
Point is exactly "halfway between" points and
Moreover, is the point at which the tangent is parallel to the secant