# Can more than four circles internally tangent or external tangent or combination of both each others at different points?

Is it true for infinite number of m, more than four, there exist m circles internally tangent or external tangent or combination of both each others(in this problem, i mean a circle must be tangent to all other circles, every two pair of circle tangent at a different point)? please prove this or disprove this.

Rephrase: Is it true that there exist (m>4) circles tangent to each other at different points?

i never got this because i never ever tried to generalize any geomertic theorem before.

Sorry for missing a piece of important but must for sure to edit it. Thanks in advance for answer it. This haven't answered for a day, can someone help?

Ignore the inner red circle, this picture is an example that fulfill the requirement in this problem:

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It's very hard to understand what your question is. Could you rephrase it? –  Lubin Apr 29 '12 at 17:33
@Lubin - You see how the circle touches in my picture? –  Victor Apr 29 '12 at 19:00
Are you asking whether there exists a set of $m$ circles which are all tangent to each other, for $m > 4$? The answer is no but I can only think of a proof using circle inversion. –  Rahul Apr 29 '12 at 19:08
@RahulNarain - Yes, but the circles are tangent to each other at a different point. –  Victor Apr 29 '12 at 19:16
@RahulNarain - if you know a proof, please answer. –  Victor Apr 29 '12 at 19:20