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Here is a comparative description of Morley triangles and cubics. This page was made with contributions by Edward Brisse. Denote by T1, T2, T3 the three Morley triangles and by T1*, T2*, T3* the three corresponding Morley adjunct triangles (see TCCT, pp. 165167, §§ 6.25, 6.26, 6.27, 6.30). IaIbIc is the excentral triangle. Perspective triangles and perspectors : 







Each point P related to T1 has a "plus" version P+ and a "minus" version P obtained when the trisectors of A, B, C are replaced by those of A+2pi, B+2pi, C+2pi and A2pi, B2pi, C2pi respectively. For example, X(1134) = X(357)+ and X(1136) = X(357). Points on the cubics : 



Related trilinear coordinates : The following table gathers together some points with first trilinear coordinate containing A/3 angles. 



Remark : the line X(16)X(358) also contains all the points with first trilinear coordinate • cos A + 2 cos B/3 cos C/3 + t cos (A/3 + u), • cos A + 2 sin B/3 sin C/3 + t cos (A/3 + u), where t and u are any real numbers. 

Other related curves : 
