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Metalworking (rec.crafts.metalworking) Discuss various aspects of working with metal, such as machining, welding, metal joining, screwing, casting, hardening/tempering, blacksmithing/forging, spinning and hammer work, sheet metal work. |
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A Planar Geometry Problem
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, Bob |
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