Dear Alexey,

In Hyacinthos message #9144, you wrote:

>> I think that I is in HaHb.

Exactly. My apologies for the typo.

In Hyacinthos message #9145, you wrote:

>> The equivalence of 2 and 5 is a particular case

>> of next fact. Let given a triangle ABC and a

>> point P. A1, B1 are the common point of AP and

>> BC, BP and AC. Q - a point in A1B1, Q' is

>> isogonally conjugated to Q, A2, B2 are the

>> common points of AQ' and BC, BQ' and AC. Then

>> the point P' isogonally conjugated to P is in

>> A2B2. This can be easily proved by trilinear

>> coordinates.

Yes, and this was exactly the same generalization

I found in 2002 when I solved the problem!

Sincerely,

Darij Grinberg