Path: utzoo!utgpu!watmath!att!pacbell!ames!eos!jbm
From: jbm@eos.UUCP (Jeffrey Mulligan)
Newsgroups: comp.graphics
Subject: Re: Tangents to Three Circles
Message-ID: <4630@eos.UUCP>
Date: 9 Aug 89 02:32:08 GMT
References: <859@mrsvr.UUCP> 
Organization: NASA Ames Research Center, California
Lines: 29

beshers@cs.cs.columbia.edu (Clifford Beshers) writes:

>In article <859@mrsvr.UUCP> hallett@mrsvr.UUCP (Jeff Hallett) writes:


>   I have an interesting geometry problem.  Given three circles, I need
>   to be able to find a circle tangent to all three.  I realize that,
>   as specified, there are upto 6 possible solutions, but there is
>   always one. 

>Do you mean, for any 3 circles a, b and c there exists a circle d
>that is tangent to each of a, b and c?  What about the case where
>a, b and c share the same center, but each has a radius different
>from the other.  I can't visualize a circle d tangent to all three.

Good counterexample.  If you accept the following lemma,
I think it is obvious that there is no solution for the case
of 3 concentric circles:

Lemma:  If circle A is tangent to circle B at point T, the the
points of A excluding T must lie either entirely inside, or entirely
outside, of circle B.


-- 

	Jeff Mulligan (jbm@aurora.arc.nasa.gov)
	NASA/Ames Research Ctr., Mail Stop 239-3, Moffet Field CA, 94035
	(415) 694-6290