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$

*

*Consider the points pair-wise, call them $A$ and $B$. Let the other
point be $C$


*Consider the circle with $AB$ as diameter and check if $C$ is within this circle.
If you consider all three possibilities, you'll find that the line joining $(0, 0)$ and $(2, 3)$ is the diameter of the required circle. The equation of the circle is
$$(x - 1)^2 + (y - \frac{3}{2})^2 = \left(\frac{\sqrt{13}}{2} \right)^2$$
It is easy to verify that the other point $(1,1)$ lies inside the above circle.
