From: rusin@washington.math.niu.edu (Dave Rusin)
Newsgroups: sci.math
Subject: Re: Help wanted on circle-through-three-points problem
Date: 21 Aug 1995 19:22:10 GMT

In article <414reh$jj6@unicorn.apana.org.au>,
 <morb@unicorn.apana.org.au> wrote:
>I'm looking for some sort of formulae or algorithm that will, when given three
>points on a cartesian plane, find the centre and radius of the circle that passes
>through those points?

Each point (x,y) is expected to satisfy the same equation  
	x^2+y^2 + A x + B y + C = 0
so plug in the three combinations of  x  and  y  to get three equations in
the three unknowns  A, B, and C. Solve (assuming the points are not
collinear). Writing the equation as
	(x + A/2)^2 + (y + B/2)^2 = (A^2+B^2)/4 - C
we see the center is at  (-A/2, -B/2)  and the  radius is  sqrt(A^2/4+B^2/4-C).

dave
(P.S. - "formulae" is plural while "algorithm" is singular, making your
sentence a bit unruly to parse.)