> Hi, > > I wrote (on Roussel's triangle): > > > I have not yet read any notification of the fact that in stead of inside > > trisectors also outside trisectors can be used. The equilateral triangle > > you get from the outside trisectors and the one you get from the inside > > trisectors are reflections of each other over the circumcenter. > > The first sentence is right, the second isn't. I don't know where I got > this from. I'm sorry.
Oh good, because the second sentence misled me into thinking that you probably meant something unusual by "outside trisectors" , and I spent some fruitless time trying to find out just what. I now take it that you just meant the usual external trisectors, namely the lines at angles of +- 120 degrees to the internal one. Then what survives of your statement is just that the algebraic conjugates of the construction also work (as of course they must).
I had in fact already referred to this when I remarked that there must be 18 Roussel triangles corresponding to the 18 Morley ones, although perhaps they coincide to some extent. [But perhaps that was in a message that didn't get sent to you?]