Dear Friends,
Seiichi Kirikami did send me another property of X(5390).
Construction:
• Let A1,B1,C1 be the vertices of the 1st Morley Triangle.
• Let La, Lb, Lc be the Euler Lines of triangles A.B1.C1, B.C1.A1, C.A1.B1.
• Then La, Lb, Lc concur in X(5390).
• The lines through A,B,C parallel to La, Lb, Lc also concur in a point.
• This point happens to be X(1136) !
When the parallel lines are drawn through the vertices of the Medial Triangle or the AntiComplementary Triangle, these lines also are concurrent, however not in ETC-points.
This parallel-construction is similar to the construction method of points X(3647) to X(3652) in ETC.
I suppose there will be more Morley related points that can be constructed this way.
Best regards,
Chris van Tienhoven
Seiichi Kirikami did send me another property of X(5390).
Construction:
• Let A1,B1,C1 be the vertices of the 1st Morley Triangle.
• Let La, Lb, Lc be the Euler Lines of triangles A.B1.C1, B.C1.A1, C.A1.B1.
• Then La, Lb, Lc concur in X(5390).
• The lines through A,B,C parallel to La, Lb, Lc also concur in a point.
• This point happens to be X(1136) !
When the parallel lines are drawn through the vertices of the Medial Triangle or the AntiComplementary Triangle, these lines also are concurrent, however not in ETC-points.
This parallel-construction is similar to the construction method of points X(3647) to X(3652) in ETC.
I suppose there will be more Morley related points that can be constructed this way.
Best regards,
Chris van Tienhoven
--- In Hyacinthos@yahoogroups.com, Antreas Hatzipolakis wrote:
>
> X(5390) = EULER-MORLEY-ZHAO POINT
>
> Barycentrics (unknown)
> Let DEF be the classical Morley triangle. The Euler lines of the three
> triangles AEF, BFD, CDE
> appear to concur in a point for which barycentric coordinates remain
> to be discovered.
> Construction by Zhao Yong of Anhui, China, October 2, 2012.
>
> http://faculty.evansville.edu/ck6/encyclopedia/ETCPart3.html
>
>
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