circle

are you sure that the question is even valid because this is what it looks like 

Let the center =  x,y

Using the square of the distance  formula  using (0,0)  and (-3, 2)

x^2 + y^2 = r^2

(x+3)^2 + (y-2)^2 = r^2       set these equal

x^2 + y^2 =  x^2 + 6x + 9  + y^2 - 4y + 4

6x - 4y =  -13     (1)

Again  using (0,0)and ( -2,1)

x^2 + y^2  = r^2

(x + 2)^2 + (y -1)^2 = r^2    

x^2 + y^2 = x^2 + 4x + 4 + y^2 - 2y + 1

4x -2y = - 5     →  -8x + 4y = 10       (2)

Add (1) ,(2)

-2x = -3

x = 3/2  

4(3/2) - 2y = -5

6 - 2y = -5

11 =2y

y =  11/2

(x, y) = (3/2, 11/2)  = (1.5, 5.5)