Due to time constraints (I'm answering a LOT of questions)....I'll provide the set up and let Wolframalpha do some magic [ if I have time later, I'll go through the process of finding the center]
Let the center be (a,b)
We have this system of equations
(2-a)^2 + (-5-b)^2 = (a-7)^2 + ( -5-b)^2
(2-a)^2 + (-5 -b)^2 = (a-6)^2 + (b-1)^2
(a - 7)^2 +(-5-b)^2 = (a -6)^2 + (b - 1)^2
The center (by WolframAlpha) is (9/2 , -7/3)
The radius^2 = ( 6-9/2)^2 + (-7/3 - 1)^2 = 481/36
radius = sqrt (481) / 6
The equation of the circumcircle is
(x - 9/2)^2 + ( y + 7/3)^2 = 481/36