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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)
*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com
*Delivered-to*: l-mathgroup@wolfram.com
*Delivered-to*: mathgroup-newout@smc.vnet.net
*Delivered-to*: mathgroup-newsend@smc.vnet.net
*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
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