Question 969935
You want to know the center of the circle which contains those three points?
You have the center at unknown point  (x,y):


{{{sqrt((x-3)^2+(y+2)^2)=sqrt((x+2)^2+(y-3)^2)=sqrt((x+6)^2+(y+5)^2)}}} which is essentially three different equations.


Using the first two members,...
{{{(x-3)^2+(y+2)^2=(x+2)^2+(y-3)^2}}}
{{{x^2-6x+9+y^2+4y+4=x^2+4x+4+y^2-6y+9}}}
{{{-6x+9+4y+4=4x-6y+9}}}
{{{-6x-4x+9+4y+4+6y-9=0}}}
{{{-10x+10y+4=0}}}
{{{highlight_green(-5x+5y+2=0)}}}


Using the last two members,...
{{{x^2+4x+4+y^2-6y+9=x^2+12x+36+y^2+10y+25}}}
{{{4x+4-6y+9=12x+36+10y+25}}}
{{{4x+4-6y+9-12x-36-10y-25=0}}}
{{{-8x-16y+4+9-36-25=0}}}
{{{-8x-16y-48=0}}}
{{{-2x-4y-12=0}}}
{{{highlight_green(x+2y+6=0)}}}


Those green-bordered equations are the system which will give the coordinates for the center point of the circle.
{{{system(-5x+5y=-2,x+2y=-6)}}}


Use 5 times the second equation, use Elimination at least part of the way.
{{{(-5x+5y)+(5x+10y)=-2+(-6)*5}}}
{{{15y=-2-30}}}
{{{15y=-32}}}
{{{highlight(y=-32/15)}}}


Find x coordinate.
{{{x=-6-2y}}}
{{{x=-6-2(-32/15)}}}
{{{x=-6+64/15}}}
{{{x=-6(15/15)+64/15}}}
{{{x=(64-6*15)/15}}}
{{{highlight(x=-26/15)}}}


Coordinates for the center are outlined in RED.