4 ms·

Why can it only touch three circles? I can draw as many tangent circles as I want to for any given path.

• bestham 9y ago
  The same reason that a table with three legs is always stable. If you add more legs it can begin to wobble depending on the smoothness of surface it stands on. The larger circle needs to touch three circles because if it touches any more two of those circles will be not change the larger circles if removed and are thus not necessary.
  • debatem1 9y ago
    I'm not sure we're saying the same thing. I'm saying that it is not true that it can only touch three (or four, or any less-than-infinite number of circles). I think you're saying that only three of them are necessary to draw the correct circle. The analogy would be that any three points on a plane describe both the vertices of exactly one triangle and exactly one circle circumscribing it (your statement) and that an infinite number of circumscribed triangles can be found for any nontrivial circle (my statement).
• mbostock 9y ago
  You can have more than three tangent circles, but three tangent circles are sufficient to represent an enclosing circle.