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RE: Fast help for circle problem

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
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
in the directory "mathematics".

-----Original Message-----
From: jmittag [mailto:jmittag at] To:
mathgroup at
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.

Thanks in advance!

Jens Mittag

email: Jens.Mittag at

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