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

Jack


                -----Original Message-----
                From:   F. Alfredo Rego [mailto:[log in to unmask]]
                Sent:   Tuesday, October 12, 1999 2:02 PM
                To:     [log in to unmask]
                Subject:        Re: OT: High School math question

                Barry Lake <[log in to unmask]> wrote:

                >At 12:07 PM -0600 10/12/99, [log in to unmask] wrote:
                > >See http://www.treasure-troves.com/math/SoddyCircles.html
for an
                > >excellent description and an excellent graphical
treatment:
                > >
                > >        Given three distinct points A, B, and C, let
three Circles
                > >        be drawn, one centered about each point and each
one tangent
                > >        to the other two...
                >
                >
                >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
                >be possible to create the inner or outer Soddy circles,
either.

                Your quibble is understandable, but check the "Given"
description
                above so that you can sleep better tonight.  Try to have
points A, B,
                and C be on *the same* line AND to have *each* circle be
tangent to
                the other two :-)

                A good mathematical statement is like a good poem: It says a
lot with
                the minimum of words.  I believe the "Given" statement above
is
                extremely elegant (and, as it should, it says a lot,
including a
                pre-answer to your quibble).


                >In any case, I have immensely enjoyed this thread
(especially the website
                >mentioned above, thanks Alfredo!).

                My pleasure, indeed.  In fact, I bought Eric's "Concise"
(ha!)
                Encyclopedia of Mathematics last year and the CD version,
which I
                carry with me all over the world (the CD, not the book :-)


                >In solving the original problem I had to
                >exercise some brain cells I forgot I had. Perhaps this will
help in my
                >"real" work...

                Good.  Oops, that's what I should be doing, instead of
playing around
                with mathematics :-)

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