what is the circle with the smallest radius that contains the three points $(0,0)$ , $(1,1)$, and $(2,3)$? How to write a model that gives us a circle with the smallest radius that contain three points $(0,0)$ , $(1,1)$, and $(2,3)$?
I've tried to model this as following:
if $x, y$  be the location and $r$ is radius:
$ Min \ \ x^2+y^2 = r^2$
$ x^2+y^2 \le 0$
$ (x-1)^2+(y-1)^2 \le 1$
$ (x-2)^2+(y-3)^2 \le \sqrt 13$

How about:
min $r^2$ subject to:
$(x-0)^2 + (y-0)^2 \leq r^2$
$(x-1)^2 + (y-1)^2 \leq r^2$
$(x-2)^2 + (y-3)^2 \leq r^2$
