> [APH]

> > Let ABC be a triangle and Ab,Ac the Orthogonal projections

> > of A on the Reflections of BH,CH in AO, resp.

> >

> > Let La be the reflection of the Euler Line of AAbAc

> > in AbAc.

> >

> > Similarly Lb, Lc.

> >

> > Are the lines La,Lb,Lc concurrent?

>

> I think they are concurrent, and also the perpendiculars

> from A,B,C to La,Lb,Lc, resp. are concurrent.

> (on the circumcircle of ABC ?)

>

> Which is the point of concurrence of La,Lb,Lc

> (1) wrt triangle ABC (2) wrt the orthic triangle of ABC

> (the lines AbAc, BcBa, CaCb bound the orthic triangle)

>

> Which is the point of concurrence of the perpendiculars?

I have uploaded to Hyacinthos files the pdf file Francisco sent

me with solutions: NAGEL POINT OF ORTHIC TRIANGLE X(185)

and KIEPERT HYPERBOLA FOCUS X(110)

I am wondering how could we get the GERGONNE point

of the orthic triangle by a similar construction

(ie by Euler lines reflected).

Probably by a locus problem like this:

Let ABC be a triangle, HaHbHc the orthic triangle,

and P a point.

Let Ab,Ac be the orthogonal projections of A

on the Reflections of BH,CH in AP.

Let La be the reflection of the Euler Line of AAbAc in HbHc.

Similarly Lb,Lc.

Which is the locus of P such that La,Lb,Lc are concurrent?

APH