АM=BM
АM=СM
Система.
{АМ^2=BM^2
{AM^2=CM^2
{(x-1)^2+(y+1)^2+(0-5)^2=(x-3)^2+(y-4)^2+(0-4)^2;
{(x-1)^2+(y+1)^2+(0-5)^2=(x-4)^2+(y-6)^2+(0-1)^2.
{(x-1)^2-(x-3)^2+(0-5)^2=(y-4)^2-(y+1)^2+(0-4)^2;
{(x-1)^2-(x-4)^2+(0-5)^2=(y-6)^2-(y+1)^2+(0-1)^2.
{(x-1-x+3)(x-1+x-3)+25=(y-4-y-1)(y-4+y+1)+16;
{(x-1-x+4)(x-1+x-4)+25=(y-6-y-1)(y-6+y+1)+1.
{2(2x-4)+9=-5(2y-3);
{3(2x-5)+24=-7(2y-5).
{4x-8+9=-10y+15;
{6x-15+24=-14y+35.
{4x+10y=14;
{6x+14y=26.
{6x+15y=21;
{6x+14y=26.
Вычитаем из первого уравнения второе:
y=-5
4х=14-10у
4х=14+50
4х=64
х=16
О т в е т. М(16;-5;0)