This is the tricircular sextic

Q014 - 4 S^2 x y z (x + y + z) (c^2 x y + b^2 x z + a^2 y z)

where S=twice the area of ABC.

(tricircular = the circular points are triple points of the curve).

Francisco Javier.

--- In Hyacinthos@yahoogroups.com, "rhutson2" <rhutson2@...> wrote:

>

> A related locus: Q such that Q and the NPCs of BCQ, CAQ, ABQ are concyclic. This would include X(13), X(14), the bicentric pair PU(5), the circumcircle intercepts of line X(5)X(523), and the point Qi (of ABC) such that I = Qi of the cevian triangle of I.

>

> Randy

>

> --- In Hyacinthos@yahoogroups.com, Antreas Hatzipolakis <anopolis72@> wrote:

> >

> > A CIRCLE:

> >

> > Let ABC be a triangle, A'B'C' the cevian triangle of I and N1, N2, N3

> > the NPC centers of IB'C', IC'A', IA'B', resp.

> >

> > The points I, N1,N2,N3 are concyclic.

> >

> > Center of the circle?

> >

> > LOCUS:

> >

> > Let ABC be a triangle, P a point, A'B'C' the cevian triangle of P and N1,

> > N2, N3

> > the NPC centers of PB'C', PC'A', PA'B', resp.

> >

> > Which is the locus of P such that the points P, N1,N2,N3 are concyclic ?

> >

> > Antreas

> >

> >

> > On Wed, Apr 17, 2013 at 1:43 AM, Antreas <anopolis72@> wrote:

> >

> > > **

> > >

> > >

> > > Let ABC be a triangle and P a point.

> > >

> > > Which is the locus of P such that the NPC center of PBC

> > > lies on the line AP ?

> > >

> > > Ceva triangle variation:

> > >

> > > Let ABC be a triangle, P a point and A'B'C'

> > > the cevian triangle of P.

> > > Which is the locus of P such that the NPC center

> > > of PB'C' lies on the line APA' ?

> > > (The I is on the locus)

> > >

> > > APH

> > >

> > >

> > >

> > >

> > >

> >

> > http://anopolis72000.blogspot.com/

> >

> >

> > [Non-text portions of this message have been removed]

> >

>