[net.math] Morley"s Itheorem

thomas@utah-gr.UUCP (Spencer W. Thomas) (12/01/83)

Here's another neat one.  Solution is not trivial, but can supposedly be
done from Euclid (I say supposedly because I solved it with vector
arithmetic).  Given ANY (scalene) triangle (the set of scalene triangles
is dense in the set of all triangles, so you will pick one with
probability 1, right?) erect equilateral triangles on all three sides
(on the outside).  Show that the triangle formed by connecting the
centers of the equilateral triangles is itself equilateral.

Have fun!

(Please don't post solutions to the net, let people work on it.  Thanks.)

=Spencer