Dear June Lester and Antreas,
[Antreas]
circle.
On the other hand, there is at least another remarkable point on it :
the isogonal of the inverse (in the circumcircle) of the isogonal of X399.
1st bary :
1/ [(4SA^2-b^2c^2)(a^2(b^2+c^2) - (b^2-c^2)^2)] ie E380 in Edward's list of
centers.
I found this point while studying the cubic Kn :
Kn and the Lester circle have in common X5,X13,X14,E380 and the circular
points at infinity.
The lines X399-X30 (the real asymptote) and X265-E380 meet at a point which
is the intersection of Kn with its real asymptote.
Best regards
Bernard Gibert
PS : the cubic Kn
Ma, Mb, Mc are the reflections of point M about BC, CA, AB.
ABC and MaMbMc are perspective iff M lies on the Neuberg cubic.
The perspector lies on Kn
[Antreas]
>Are there any other than O,N,F1,F2 points [in the current version of ETC]according to Edward's catalogues, there is no other ETC center on the Lester
>lying on this circle?
circle.
On the other hand, there is at least another remarkable point on it :
the isogonal of the inverse (in the circumcircle) of the isogonal of X399.
1st bary :
1/ [(4SA^2-b^2c^2)(a^2(b^2+c^2) - (b^2-c^2)^2)] ie E380 in Edward's list of
centers.
I found this point while studying the cubic Kn :
Kn and the Lester circle have in common X5,X13,X14,E380 and the circular
points at infinity.
The lines X399-X30 (the real asymptote) and X265-E380 meet at a point which
is the intersection of Kn with its real asymptote.
Best regards
Bernard Gibert
PS : the cubic Kn
Ma, Mb, Mc are the reflections of point M about BC, CA, AB.
ABC and MaMbMc are perspective iff M lies on the Neuberg cubic.
The perspector lies on Kn
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