Dear Paul and Bernard

> > [PY] Given a point P, can you find a point Q so that the

centroids of

> > the cevian triangle of Q is the same as the centroid of

anticevian

> > triangle of P?

> >

> > [BG]: There are at most three such points Q.

> > one of them is aP/G (cevian quotient or Ceva conjugate) where

aP is

> > the anticomplement of P.

> > *** If there are at most three such points and one of them is

known,

> > it seems that the other two can be described as the

intersections ofÂ

> > a conic and a line.

They are the common points of the circumconic with center P and the

trilinear polar of i.h.i(q) where q = aP/G, i = isotomic

conjugation, h = homothecy (G,1/4).

Friendly. Jean-Pierre