NetNews Usenet Archive 1992 #20/NN_1992_20.iso/spool/sci/math/11165

Internet Message Format | 1992-09-09 | 1.2 KB

Path: sparky!uunet!usna!dfr
From: [e-mail] (PROF D. Rogers (EAS FAC))
Newsgroups: sci.math
Subject: Re: Help: inscribed circle of three circles
Message-ID: <[e-mail]>
Date: 9 Sep 92 16:35:56 GMT
References: <[e-mail]>
Sender: [e-mail]
Organization: U. S. Naval Academy
Lines: 26

In article <[e-mail]> [e-mail] (Gabor M. Czako) writes:
!In a computer program I am writing I need to find the inscribed
!circle(s) of three circles.  In detail, I have three circles with
!centers (x_1, y_1), (x_2, y_2), and (x_3, y_3) and radii r_1, r_2,
!r_3.  I need to find the inscribed circle(s) with center (x, y) and
!radius r which satisfies the following equations:
!
!    (x - x_1)^2 + (y - y_1)^2 = (r + r_1)^2
!    (x - x_2)^2 + (y - y_2)^2 = (r + r_2)^2
!    (x - x_3)^2 + (y - y_3)^2 = (r + r_3)^2
!
!I have not been able to analytically solve for the 0, 1, or 2
!solutions of x, y, and r.

G'day Gabe,

Look at the following paper:

Rogers, David R., Interactive graphics and numerical control,
CAD Journal pp 253-261, Vol 12 No 5 Sept 1980.

This problem as well as many others of this type are solved
for and discussed.

Dave Rogers