14756ÈÝìá: Re: [EMHL] Construction
- Jan 14, 2007Dear Nikolaos
> > > [ND] How can we construct the two linesYour points are the homothetic of the focii of the Steiner
> > > given by the equation in barycentrics:
> > >
> > > CyclicSum (SA*SA*(SB-SC)xx + 2SB*SC*(SB-SC)yz) = 0
> > 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?
circumellipse in (L,3/2) where L = de Longchamps point.
For both points, AA' = 3.T/2 where T = semimajor axis of the ellipse.
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