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