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
Yes, and this was exactly the same generalization
I found in 2002 when I solved the problem!