HYACINTHOS 7868

 

Antreas P. Hatzipolakis

Let ABC be a triangle, HaHbHc its orthic triangle
and P a point.

Which is the locus of P such that the reflections
of PHa, PHb, PHc in HHa, HHb, HHc, resp
are concurrent?

If the locus is the whole plane,
then which is the locus of the point of
concurrence, if P moves on a notable line (OH, OK,...)?

Now, let P, P* be two isogonal points
and PaPbPc the pedal triangle of P.

Which is the locus of P such that the reflections of
P*Pa, P*Pb, P*Pc in PPa, PPb, PPc, resp.
are concurrent?

(Variations: isotomic instead of isogonal;
cevian instead of pedal)


Greetings from Athens

APH