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

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Larry Cusick

Posts: 5
Registered: 12/6/04
Re: A Theorem concerning the Trisectors of a Triangle
Posted: Sep 13, 1998 10:00 PM
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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
the others, I have not found any proofs.

-Larry Cusick
CSU Fresno





Date Subject Author
9/12/98
Read A Theorem concerning the Trisectors of a Triangle
Den Roussel
9/12/98
Read Re: A Theorem concerning the Trisectors of a Triangle
John Conway
9/13/98
Read Re: A Theorem concerning the Trisectors of a Triangle
Larry Cusick
10/27/98
Read Re: A Theorem concerning the Trisectors of a Triangle
John Conway
9/13/98
Read Re: A Theorem concerning the Trisectors of a Triangle
steve sigur
9/14/98
Read Re: A Theorem concerning the Trisectors of a Triangle
John Conway
9/15/98
Read Re: A Theorem concerning the Trisectors of a Triangle
John Conway
9/15/98
Read Re: A Theorem concerning the Trisectors of a Triangle
Richard Guy
9/15/98
Read Re: A Theorem concerning the Trisectors of a Triangle
John Conway
9/15/98
Read Re: A Theorem concerning the Trisectors of a Triangle
Richard Guy
9/15/98
Read Re: A Theorem concerning the Trisectors of a Triangle
Richard Guy
9/16/98
Read Re: A Theorem concerning the Trisectors of a Triangle
Floor van Lamoen
9/16/98
Read Re: A Theorem concerning the Trisectors of a Triangle
John Conway
9/17/98
Read Re: A Theorem concerning the Trisectors of a Triangle
Floor van Lamoen
9/17/98
Read Re: A Theorem concerning the Trisectors of a Triangle
John Conway
9/17/98
Read Re: A Theorem concerning the Trisectors of a Triangle
Floor van Lamoen
9/17/98
Read Re: A Theorem concerning the Trisectors of a Triangle
Russell Towle
9/17/98
Read Re: A Theorem concerning the Trisectors of a Triangle
John Conway
9/17/98
Read Re: A Theorem concerning the Trisectors of a Triangle
Russell Towle
9/17/98
Read Re: A Theorem concerning the Trisectors of a Triangle
Douglas J. Zare
9/19/98
Read Re: A Theorem concerning the Trisectors of a Triangle
Russell Towle
9/20/98
Read Re: A Theorem concerning the Trisectors of a Triangle
John Conway
9/20/98
Read Re: A Theorem concerning the Trisectors of a Triangle
John Conway
9/18/98
Read Re: A Theorem concerning the Trisectors of a Triangle
Antreas P. Hatzipolakis
11/10/98
Read Re: A Theorem concerning the Trisectors of a Triangle
Den Roussel

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