NetNews Usenet Archive 1992 #20/NN_1992_20.iso/spool/sci/math/11110

Internet Message Format | 1992-09-08 | 999 b

Xref: sparky sci.math:11110 comp.graphics:9513
Path: sparky!uunet!stanford.edu!rutgers!igor.rutgers.edu!yoko.rutgers.edu!czako
From: [e-mail] (Gabor M. Czako)
Newsgroups: sci.math,comp.graphics
Subject: Help: inscribed circle of three circles
Message-ID: <[e-mail]>
Date: 8 Sep 92 13:46:27 GMT
Followup-To: sci.math
Organization: Rutgers Univ., New Brunswick, N.J.
Lines: 16

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.

Any help would be greatly appreciated.

Gabe