restart:

with(LinearAlgebra):

A:=<4,-1,-2>: B:=<0,2,3>: C:=<2,0,1>: M:=x*A+y*B+z*C:

solve({Norm(A-M,2)=Norm(B-M,2), Norm(C-M,2)=Norm(B-M,2), x+y+z = 1}): assign(%):

'M'=convert(M,list);

We find the coordinates of M.

The apparent error of Maple! I did the same example using the command Optimization [Minimize] . The result is also wrong!

Checked the calculation of the minimum by the second method. The result again is false:

Download minimum.mws

Such non-linear systems are usually solved numerically for given values ​​of all parameters! Note that parameter m on the right side of the first equation must be equal to 0, otherwise it would be contrary to the initial conditions.

Similarly, you can do the same with the second function!

Download Change_of_variable.mw

Instead of y:=unapply(f):  should be y:=unapply(f,x):

Use the command expand:

B1 := [1, 2, 0, -1]:       B2 := [0, 1, -1, 0]:                         

A1 := expand(a*B1+b*B2);                                

A1 := [a, b + 2 a, -b, -a]

In accordance with the syntax of Maple should be

Int(subs(x=1/t,expression)*(-1/t^2), t)

Apparently, you need to make the change of variable in the integral by the formula t = 1 / x. Then it will be necessary to write

Int(expression(x=1/t)*(-1/t^2), t)

DelBar2.mw 

 Here is the code, where only one joint edge of  adjacent polygons of the same color is deleted!

DelBar.mw

Download DelBar.mw

Since Your differential equation is of second order, we need another initial condition! Therefore, it is  impossible to plot your function, because there is an arbitrary constant.

See an option of solving your problem in file The_plot.mw

Thanks all for help in solving of the problem!