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Re: Apollonius' circle tactation

• To: mathgroup at smc.vnet.net
• Subject: [mg129643] Re: Apollonius' circle tactation
• From: Narasimham <mathma18 at gmail.com>
• Date: Sat, 2 Feb 2013 01:16:07 -0500 (EST)
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• References: <ke7uhb$4i2$1@smc.vnet.net>

On Jan 29, 12:42 pm, "Dr. Heinz  Schumann" <schuman... at web.de> wrote:
> Dear Colleagues,
> does exist a veritable and short Mathematica solution of the problem to calculate the midpoint coordinates and the radius of a third (fourth) circle tangent to two (three) given circles already mutual tangent.
> Best
> Heinz Schumann

1) Google " Kiss precise " for Soddy circles in general.

 2) Hint: Using 1/d = 1/a+1/b+1/c+ 2*Sqrt[(a+b+c)/(a*b*c)] above ,
find d.

Center of circles radii a, b are foci in a bipolar coordinate system.
Find Apollonius circle locus for constant ratio of sides ( a + d )/( b
+ d ), pairwise, to find the center of inward contact of all circles.

Narasimham