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>,
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.)