At 12:13 PM -0700 10/12/99, [log in to unmask] wrote:
>> My only quibble with this (and it's a small quibble, indeed) is if points
>> A, B, and C all happen to be on the same line, then it won't be possible to
>> draw three such circles each tangent to the other two. Therefore, it won't
>
>Sure they can...assume 3 co-linear points, with the middle point equidistant
>between the other two:
>
>              A      B      C


As usual, Stan is "thinking outside the box" again. (or should I say
"outside the circle" (or, in this case *inside* the circle ;-)  )).

The rules of the particular box in which I had voluntarily placed myself
did not allow for any of the circles to contain the others. In other words,
"inside tangency" wasn't allowed. Lifting that rule lets Stan's corner case
be true.

In that case, *two* smaller circles could be drawn that are "tangent" to
the other three, but they would be outside two of them (centers A and C),
and inside the larger one (center B). I'm not sure if they still qualify as
"inner Soddy circles", though. Also, in this case, then, the largest circle
(center B) would serve double duty as the "outer Soddy circle". But I
digress (as do we all!)...

BBL