14758Θέμα: Re: [EMHL] Construction
- Jan 14, 2007Dear Jean-Pierre,
> > > I tried to find for which points P the pedal
> > > 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
> > > From a sketch it seems to exist only two such
> > > on one of these lines.
> > > Can we construct these points?
> > Your points are the homothetic of the focii of the
> > circumellipse in (L,3/2) where L = de Longchamps
> > For both points, AA' = 3.T/2 where T = semimajor
> axis of the
> A little explanation :Excellent!
> it is well known that the focii of the Steiner
> circumellipse have
> cevian of equal lengths.
> As they lie on the Lucas cubic, their cevian
> triangles are the pedal
> triangles of the required points
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