Dear Bernard and Nikolaos

Thanks you very much for your responses

It will be useful for me

Amically

Michel

--- In

Hyacinthos@yahoogroups.com, Nikolaos Dergiades <ndergiades@...>

wrote:

>

> Dear Michel

> I don't know to answer your question.

> This conic also becomes a circle if M = X(194)

> the anticomplement of the isotomic conjugate

> of the Lemoine point X(6).

> If have no error it becomes a parabola if M lies on the quartic

> 3(x^4+y^4+z^4)-2(x^3+y^3+z^3-xyz)(x+y+z)-5(xy+yz+zx)^2=0

> Best regards

> Nikos Dergiades

>

>

> > Dear Hyacinthos

> > In triangle (ABC), point M= [m:n:p] has for cevian triangle

> > (PQR),

> > with P =[0:n:p], Q = [m:0:p], R=[m:n:0]

> > Parallel line through P to (AC) cuts (AB) in Cp = [p:n:0]

> > Parallel line through P to (AB) cuts (AC) in Bp = [n:0:p]

> > So are Aq,Cq,Ar,Br

> > Those six points lie on a same conic with barycentric

> > equation

> > np uÂ²+mpvÂ²+mnwÂ²-(mÂ²+np)vw-(nÂ²+mp)wu-(pÂ²+mn)uv = 0

> > If F is the centroÃ¯d of (ABC), this conic is the inscrit

> > conic of

> > Steiner, with center G

> > file "conique1" with figure is add to the forum

> >

> > Is that known in math litterature?

> >

> > Amically

> >

> > Michel

> >

> >

> >

> >

> > ------------------------------------

> >

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