It sounds like what you need to do is do a little algebra, to convert the equations in the Math Forum article into a different set of equations that express the unknowns you're solving for (h, k and r) in terms of the coordinates of your three points (x1, y1, x2, y2, x3, and y3).  In other words, you want to manipulate those equations using algebra, until they have the form:

  h = blah blah blah;
  k = blah blah blah;
  r = blah blah blah;

Where the "blah blah blahs" are actually formulas containing the coordinates of your points.

The article actually tells you how do to that here:

"First subtract the third equation 
from the other two, thus eliminating r^2, h^2, and k^2. That will 
leave you with 2 simultaneous linear equations in h and k to solve."

This means you have to expand out the equations, like this:

(x1-h)^2 + (y1-k)^2 = r^2
becomes
(x1^2 - 2*h*x1 + h^2) + (y1^2 - 2*k*y1 + k^2) = r^2

And the same for the other two.

Once you subtract your third equation from the other two, the r^2, h^2 and k^2 terms all cancel each other out.
This leaves you with two equations that are "linear in h and k", which means you can combine them again, and
make two new equations, one for h, and one for k, that express them solely in terms of all your x1's and y1's, etc.  

Here's an explanation of how to solve simultaneously for two variables using two linear equations:
http://www.themathpage.com/alg/simultaneous-equations.htm

Follow those instructions, and you should be able to figure out what the "blah blah blahs" should be!

@eltodesukane 

So, I've created code as best I could to represent the algebra found on that page, and it isn't working as expected.