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Topic: A Theorem concerning the Trisectors of a Triangle
Replies: 24   Last Post: Nov 10, 1998 12:19 AM

 Messages: [ Previous | Next ]
 Larry Cusick Posts: 5 Registered: 12/6/04
Re: A Theorem concerning the Trisectors of a Triangle
Posted: Sep 13, 1998 10:00 PM

Den Roussel wrote:
>While investigating the Morley triangle, I came upon this theorem which
>some might find interesting.
>
> If the Angular trisectors of a triangle
>are produced to the Circumcircle , then the Chords of adjacent
>trisectors form an Equilateral triangle.
>
>It has been suggested that this result might follow from Morleys
>theorem. So far, I have been unable to make this connection. Any
>thoughts ?
>
>Den Roussel

Here is another Morley triangle oddity. Take the six triangles around the
Morley triangle (formed by not erasing the segments from the vertices of
the original triangle to the morely triangle) and call the respective
incenters of these six triangles A, B, C, D, E, F (moving say clockwise
around). Then the three segments AD, BE and FC are concurrent. (I don't
know how to prove this). The same is true for circumcenters and centroids
(but not orthocenters). The proof for centroids is easy--infact it has
nothing to do with the Morley triangle (any other triangle will do). As for

-Larry Cusick
CSU Fresno

Date Subject Author
9/12/98 Den Roussel
9/12/98 John Conway
9/13/98 Larry Cusick
10/27/98 John Conway
9/13/98 steve sigur
9/14/98 John Conway
9/15/98 John Conway
9/15/98 Richard Guy
9/15/98 John Conway
9/15/98 Richard Guy
9/15/98 Richard Guy
9/16/98 Floor van Lamoen
9/16/98 John Conway
9/17/98 Floor van Lamoen
9/17/98 John Conway
9/17/98 Floor van Lamoen
9/17/98 Russell Towle
9/17/98 John Conway
9/17/98 Russell Towle
9/17/98 Douglas J. Zare
9/19/98 Russell Towle
9/20/98 John Conway
9/20/98 John Conway
9/18/98 Antreas P. Hatzipolakis
11/10/98 Den Roussel