Since we are given three points on the circle, and we know that each point is a distance equal to the radius to some point (x,y), we can set up a system of equations to solve for the center...
Knowing that the distance between any two points is:
d^2=(x2-x1)^2+(y2-y1)^2 and these distances are all equal we can say
d^2=(x-0)^2+(y-0)^2, (x+3)^2+(y-0)^2, (x-1)^2+(y-2)^2
d^2=x^2+y^2, x^2+6x+9+y^2, x^2-2x+1+y^2-4y+4 now getting differences
0=-6x-9, 8x+4+4y
Since both of the equations above are equal to zero we can see that:
-6x-9=0
-6x=9
x=-9/6
x=-1.5, making 8x+4+4y=0 become:
8(-1.5)+4+4y=0
-12+4+4y=0
-8+4y=0
4y=8
y=2
So the center of this circle is at the point (-1.5, 2)
