Re: [EMHL] Two equivalent theorems (an old and a new(?))

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• - ... (resp.) ... Dear Attreas! This is evident. The lines AA , BB , CC are parallel, so their reflections concur in the point isogonally conjugated to
Message 1 of 2 , Feb 5, 2004
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->
>NEW(?) THEOREM:
>Let A', B', C' be the orthogonal projections of A,B,C on the line HP.
>The reflections of AA', BB', CC' in the angle bisectors AA*, BB*, CC*
(resp.)
>of ABC concur at P' on the circumcircle of ABC.
>
Dear Attreas!
This is evident. The lines AA', BB', CC' are parallel, so their reflections
concur in the point isogonally conjugated to infinite.

Sincerely Alexey
• ... HP. ... CC* ... reflections ... Dear Alexey, Yes, this is obvious for the general case (ie for an arbitrary line) But in the special case, ie for a line
Message 2 of 2 , Feb 6, 2004
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[APH]:
> >NEW(?) THEOREM:
> >Let A', B', C' be the orthogonal projections of A,B,C on the line
HP.
> >The reflections of AA', BB', CC' in the angle bisectors AA*, BB*,
CC*
> (resp.)
> >of ABC concur at P' on the circumcircle of ABC.
> >
[AZ]:
> This is evident. The lines AA', BB', CC' are parallel, so their
reflections
> concur in the point isogonally conjugated to infinite.

Dear Alexey,

Yes, this is obvious for the general case (ie for an arbitrary line)
But in the special case, ie for a line passing through H,
the isogonal conjugate is the SAME point we get with the OLD theorem
in my first message.

Greetings

Antreas
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