If you rewrite the equation of the a circle at {x0,y0} with radius R0 in the following form:
x^2 + y^2 = (x0^2 + y0^2 -R0^2) + (2* x0) * x +(2*y0) * y (* z = c + a * x + b * y *)
where {x,y} are points on the circumference. You can use the linear model fit to find the circle
In[23]:= (reg={2 #1,2 #2,#2^2+#1^2}&@@@points)//Short
Out[23]//Short= {{124,1042,275285},{132,1030,269581},{132,1044,276840},<<50295>>,{1756,1016,1028948},{1760,968,1008656}}
In[28]:= lm=LinearModelFit[reg,{1,x,y},{x,y}]
Out[28]= FittedModel[-323255.+471.705 x+501.105 y]
Best model fit by least square:
In[25]:= bf=lm["BestFitParameters"]
Out[25]= {-323255.,471.705,501.105}
In[26]:= exp=(x-#2)^2+(y-#3)^2-#1-#2^2-#3^2&@@bf
Out[26]= -150357.+(-471.705+x)^2+(-501.105+y)^2
The code is modified from this stack exchange page
