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MathGroup Archive 1998

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Re: Fast help for circle problem

  • To: mathgroup at
  • Subject: [mg13327] Re: [mg13261] Fast help for circle problem
  • From: MJE <evans.nospam at>
  • Date: Mon, 20 Jul 1998 02:49:49 -0400
  • Organization: None
  • References: <>
  • Sender: owner-wri-mathgroup at

Funny thing -- a fellow engineer asked me this same type of question a
few months ago.  This is a classic four-bar linkage problem.  Look up
the answer in a dynamics textbook.  The four bars are joined at the
centers of the circles.


Mark E.

jmittag wrote:
> 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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