Dear Nikolaos

> > > [ND] How can we construct the two lines

> > > given by the equation in barycentrics:

> > >

> > > CyclicSum (SA*SA*(SB-SC)xx + 2SB*SC*(SB-SC)yz) = 0

>

> [BG]

> > these are the parallels at H to the asymptotes of

> > the Kiepert hyperbola.

>

> Thank you very much.

> These are the parallels from H to the Simson

> lines of the points where the Brocard axis meets

> the circumcircle.

>

> I tried to find for which points P the pedal triangle

> of P A'B'C' has vertices equidistant from A,B,C

> i.e. AA' = BB' = CC'.

> These points must be symmetric wrt H.

> I found that these points must be on these lines.

> From a sketch it seems to exist only two such points

> on one of these lines.

> Can we construct these points?

Your points are the homothetic of the focii of the Steiner

circumellipse in (L,3/2) where L = de Longchamps point.

For both points, AA' = 3.T/2 where T = semimajor axis of the ellipse.

Friendly. Jean-Pierre