HYACINTHOS 17901

Let ABC be a triangle and A'B'C' its orthic triangle.

Denote:

Ab := The Orthogonal Projection of A' on AC

aB := The Orthogonal Projection of A' on CC'

Ac := The Orthogonal Projection of A' on AB

aC := The Orthogonal Projection of A' on BB'.

[The 4 points are collinear]

La := The Euler Line of A'AbAc

Ma := The Euler Line of A'aBaC

Similarly Eb, Ec and Mb, Mc.

We know that Ea,Eb,Ec concur at X(973) and Ma, Mb, Mc
at the Feuerbach point of A'B'C'

Now, denote:

A* := La /\ Ma, B* := Lb /\ Mb, C* := Lc /\ Mc

Conjecture:

The triangles ABC, A*B*C* are homothetic.

If so, which is the homothetic center
(perspector of ABC, A*B*C*) ?


Antreas