"Bailie, Jack" <[log in to unmask]> wrote:

>You can easily satisfy the given by placing two smaller circles inside a
>larger one with all three centers on a line.

Indeed.  All three circles touch in a single point (sonic-boom like?)
and each circle is tangent to the other two.  A very pretty graphic.
I had not considered this possibility.  Good job!

I wonder whether the "given" condition should then specify the "side"
of the tangency ("from the inside" or "from the outside") along the
following lines.  If "[all? circles] tangent from the outside" (as I
saw it), it is possible to have an inner Soddy circle; if "[some?
circles] tangent from the inside" (as Jack saw it), it is not, at
least in a non-imaginary way.  I haven't had time to polish these
"inside/outside" tangency statements to be as precise as they could,
so please bear with me, but I hope the drift is there and I hope a
younger and fresher mind can take the topic to its logical end so we
can help Jeff as much as possible :-)

Even though these kinds of thoughts might appear "off topic", they
are actually quite ON topic.  We need the same kind of "analysis of
the question" (and of "the given") to decide, for instance, whether
to use a high-performance IMAGE database under MPE/iX or a generic
one under a generic operating system :-)


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