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too complicated to be written here. Click on the link to download a text file.

X(3), X(20), X(30), X(1498), X(3184), X(5897), X(11589), X(11744), X(15478)

vertices of the cevian triangle of X(20)

other points below

Geometric properties :

K1349 = pK(X3284, X20) is a pK having the same infinite points as the Neuberg cubic K001, namely X(30) and the circular points at infinity. See further details in page K1348.

These two cubics meet again at A, B, C, O and two (very complicated) points N1, N2 that lie on the line {112, 376, 577, 1249, 1294, 3163, 3184, etc} and on the circum-conic with perspector X(520) passing through {2, 3, 97, 276, 394, 1073, 1214, 1217, 1297, 2416, etc}.

These points are now X(59484), X(59485) in ETC. Obviously, their isogonal conjugates also lie on K001.

The singular focus of K1349 is X(15647), the midpoint of {20,11744}, {74,1498} and others.

Points on K1349

Q1 = {20,11744} /\ {1498,5897}, tangential of X(30)

Q2 = {30,5897} /\ {11589,11744}, X(20)-Ceva conjugate of X(11744)

T = tangential of X(30) = X(20)-Ceva conjugate of Q1