Question 1022551
The three points A, B, C, also form three chords of the circle.  The perpendicular bisectors will intersect in the center of the circle.  The distance from the center to any of point A, B, or C will be the size of the center, r.  Use the Distance Formula.


Find those and you can fill in the standard form circle's equation {{{(x-h)^2+(y-k)^2=r^2}}}.



---


Some of the work toward the solution:



Perpendicular Bisector Line to A and B
{{{m=-(2+2)/(3-5)=-4/(-2)=2}}};
Through midpoint {{{system(x=0,y=(3+5)/2=8/2=4)}}}  or the point  (0,4);
{{{y=2x+4}}}.




Perpendicular Bisector Line to B and C
{{{m=-(-2-4)/(5+1)=-(-6)/6=1}}};
Through midpoint {{{system(x=(-2+4)/2=1,y=(5-1)/2=4/2=2)}}}   or the point  (1,2);
{{{y-2=1*(x-1)}}}
{{{y=x-1+2}}}
{{{y=x+1}}}




Center point (h,k) is the intersection or solution of the system {{{system(y=2x+4,y=x+1)}}}.
-
MORE----------------------
-
{{{2x+4=x+1}}}
{{{x+4=1}}}
{{{x=1-4}}}
{{{x=-3}}}
-
{{{y=x+1}}}
{{{y=-3+1}}}
{{{y=-2}}}
-
Center of circle (h,k) is  (-3,-2).