We can naturally ask the same question for the NPCs of the same triangles ie

Which is the locus of P such that the NPCs of the pedal triangle of P and

the NPC of the antipedal triangle of P are tangent

but probably the locus, if exists, is too complicated!!

More simple becomes the locus, if we replace the pedal triangle's NPC with

the NPC of the antipedal triangle of the isogonal conjugate of P,

that is:

Let ABC be a triangle and P, P* two isogonal conjugate points.

Which is the locus of P such that the NPCs of the antipedal

triangles of P and P* are tangent.

I guess that the locus is McCay cubic +???????

And if we replace the tangency of the circles with the orthogonal intersection,

the locus will be Kjp + ???? ????

Just some midnight thoughts!!! ..... :-)

APH

On Thu, Mar 14, 2013 at 11:13 PM, Antreas Hatzipolakis

<

anopolis72@...> wrote:

> Are there real points P such that the pedal and antipedal circles of P

> are tangent?

>

> APH