On 05/03/2011 02:44 PM, Bob Engelhardt wrote:
First: in general, it is not solvable. There are points which cannot lie
on a circle tangent to two others. E.g., the point cannot be inside
either circle. And there are 4 other, "small", areas that are difficult
to describe, but are easily shown on a graphic (later).

Second, and more importantly, the radius of the solution circle can
approach infinity. So, in practical terms, it becomes unsolvable at some
point, depending upon whether you are using CAD or a drawing board G.

Now, there are three cases for the solution: where the given circles are
externally or internally tangent to the solution circle, or one of each.
Do your problems always fall into one of these classes? Also, if the
given circles can overlap, it may be a different set of solution classes
(I haven't thought that through). Do your circles ever overlap?

I love plane geometry,

I generally love plane geometry, but this has me stumped -- at least as
a compass-and-straightedge problem.

The immediate problem is for making pseudo-ellipsis in a cheap CAD
program (Qcad), so one could even restrict the two 'master' circles to
being the same diameter. But there are times when I'd like to use
different sized circles for this (imagine a triangle with rounded
corners, and 'puffy cheeks').

I can see an algebraic approach for this involving over use of the
Pythagorean theorem, but I'd rather know if there's a solution that can
be done by construction, not by numbers.

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Do you need to implement control loops in software?
"Applied Control Theory for Embedded Systems" was written for you.
See details at http://www.wescottdesign.com/actfes/actfes.html