RE: Fast help for circle problem

• To: mathgroup at smc.vnet.net
• Subject: [mg13334] RE: [mg13261] Fast help for circle problem
• From: "Jean-Marie THOMAS" <jmthomas at cybercable.tm.fr>
• Date: Mon, 20 Jul 1998 02:49:54 -0400
• Sender: owner-wri-mathgroup at wolfram.com

```I wrote recently solutions to a similar problem: given a set of positive
real numbers, representing the radii of circles, how can I draw these
circles in such a way that they never overlap and keep as compact as
possible.
They are multiple solutions, depending on whether to keep the sorting
order of the set of numbers. The constrain on compactness has been a
prerequisite at the beginning of my work, but abandoning this constrain
leads to other sets of solutions, with a fractal-like behaviour. Mail
me if interested, I guess I can give you interesting tips and
eventually computational geometry packages. Have a look at
ftp://tea.fr.eu.org
in the directory "mathematics".

-----Original Message-----
From: jmittag [mailto:jmittag at pc0932g1.bv.tu-berlin.de] To:
mathgroup at smc.vnet.net
Subject: [mg13334] [mg13261] Fast help for circle problem

We are looking for a solution for the following problem:

Given are 3 circles, each with center coordinates and radius. Circle 1
is touching circle 2 and circle 2 is touching circle 3 (without any
intersection). As a special case circle 1 is also touching circle 3.

We are looking for circle 4, which is touching circles 1 to 3.

The equation for one circle "i" is as follows:

(ri+r4)^2=(x4-xi)^2+(y4-yi)^2   with i = 1,2,3

We need a symbolic solution for x4, y4 and r4.