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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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John Conway

Posts: 2,238
Registered: 12/3/04
Re: A Theorem concerning the Trisectors of a Triangle
Posted: Oct 27, 1998 2:56 PM
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Somehow I forgot to reply to this:

On Sun, 13 Sep 1998, Larry Cusick wrote:

> 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.


I think I can see my way to proving at least some of these results,
but only using barycentric coordinates. Anyway, I'll have a try.
John Conway




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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