functions - Code to give center of circle given three points in 2D?

Does anyone know how to make a function like this:

C(p1,p2,p3)=center of circle that goes through p1, p2, and p3?

This is in 2D

Answer

I have this old converted code stashed away here, but it isn't very good. I don't know how to handle the case where the points are collinear... Perhaps someone can improve on this and make it more Mathematica-y.

circleThrough3Points[{p1_, p2_, p3_}] := 
 Module[{ax, ay, bx, by, cx, cy, a, b, c, d, e, f, g, centerx, 
   centery, r},
  {ax, ay} = p1;
  {bx, by} = p2;

  {cx, cy} = p3;
  a = bx - ax;
  b = by - ay;
  c = cx - ax;
  d = cy - ay;
  e = a (ax + bx) + b (ay + by);
  f = c (ax + cx) + d (ay + cy);
  g = 2 (a (cy - by) - b (cx - bx));
  If[g == 0, False,
   {centerx = (d e - b f)/g,

    centery = (a f - c e)/g, 
    r = Sqrt[(ax - centerx)^2 + (ay - centery)^2]
    }];
  {centerx, centery, r}]

In action:

Manipulate[
 {centerx, centery, radius } = circleThrough3Points[{p1, p2, p3}];
 Graphics[
  {White,

   Rectangle[{-100, -100}, {100, 100}],
   Black,
   Circle[{centerx, centery}, radius]
   }
  ],
 {{p1, {0, 50}}, Locator},
 {{p2, {50, 50}}, Locator},
 {{p3, {50, 0}}, Locator},
 ContentSize -> {250, 250}]