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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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