14678Θέμα: [EMHL] Re: Locus of Simson line intersection point
- Jan 1, 2007Dear Jean-Pierre,
Thank you very much.
> > many thanks for your nice mails about this*********
> > You've probably noticed that when the angle of the
> Simson lines is
> > Pi/3, we get a nice trifolium inscribed in the
> circle(N,R) N = NP-
> > With N as pole and a tangent at a cusp of the
> Steiner deltoid as
> > axis, the trifolium has polar equation rho =
> Some remarks about this trifolium :
> The vertices - contact points with the circle(N,R) -
> are the vertices
> of the equilateral triangle bounded by the Simson
> lines of the
> vertices of the circumnormal triangle; these Simson
> lines are the
> common tangents of the Steiner deltoid and the
> NP-circle at the
> points where they touch each other.
These points are found by drawing from N parallells
to the bisectors of Morley's triangle.
> These vertices********
> are homothetic of
> the cusps of the Steiner deltoid in (N,2/3)
> The rectangular circumhyperbola through N intersects
> the circle (N,R)
> at 4 points; one of them is the antipode of N on the
> hyperbola; the
> three other ones are the vertices above.
Happy New Year to you and all Hyacinthists.
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