7419For the Russian members (was: Thebault point)
- Aug 3, 2003Dear all,
In Hyacinthos message #7410, I wrote:
>> >> > (1b) The Euler lines of triangles AB'C', BC'A',I think that a synthetic proof (in Russian) can be found at
>> >> > CA'B' concur at one point on the
>> >> > nine-point circle of triangle ABC.
>> >> > and (1b) is a result of Victor Thebault.
>> >> Notethat the common point is the center of
>> >> Jerabek hyperbola.
>> I have met this before. The point M where the Euler lines
>> of triangles AB'C', BC'A', CA'B' meet has the property
>> that one of the equations MA' = MB' + MC' or cyclically
>> holds. This was stated by Thebault. Can anybody find a
>> SYNTHETIC proof?
Alas, I cannot follow the author's observation. Anybody who
PS: Thanks Jean-Pierre, perhaps your equations can be
helpful in finding a synthetic proof.
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