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X(1), X(40), X(164), X(399), X(517), X(1276), X(1277), X(5541), X(11752), X(11789), X(66059), X(70227), X(71678), X(71679), X(73197), X(73198), X(73199), X(73200), X(73201)

vertices of the excentral triangle

Geometric properties :

(See ETC, preamble just before X(73197))

Let P be a point and let Pa, Pb, Pc be its reflections in the sidelines of the excentral triangle IaIbIc, anticevian triangle of the incenter X(1).

PaPbPc and IaIbIc are perspective (at Q) if and only if P lies on K1459 which is the Neuberg cubic of the excentral triangle IaIbIc.

The locus of Q is therefore K1460, the cubic K060 of this triangle.

Peter Moses notes that K1459 is also the excentral polar circle inverse of K206.

Remark : when the excentral triangle is replaced by the orthic, ITB, medial triangles, we obtain K050, K1105, K1297 respectively.