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X(6), X(32), X(98), X(184), X(232), X(237), X(511), X(9419), X(9468), X(36213), X(52177), X(70602), X(70603), X(70604)

vertices of the cevian triangle of X(6)

infinite points of the circumconic with perspector X(3051) passing through X(99), X(1576), X(1634), etc

isogonal conjugates of the infinite points of the Steiner ellipse, these points lie on the Lemoine axis and on the circumcircle

other points below

Geometric properties :

The cevian triangle of P is perspective to the circumcevian triangle of X(237) if and only if P lies on K1404.

When "cevian" is replaced by "anticevian", the locus is K380.

K1404 conains :

• P1 = a^2 (a^2+b^2-c^2) (a^2-b^2+c^2) (a^2 b^2-b^4+a^2 c^2-c^4) (a^8-2 a^6 b^2+a^4 b^4-2 a^6 c^2+a^4 b^2 c^2+b^6 c^2+a^4 c^4-2 b^4 c^4+b^2 c^6) : : , the X(6)-Ceva conjugate of X(232), on the lines {32,98}, {232,237}, SEARCH = 2.43403102934989.

• P2 = (a^4+b^4-a^2 c^2-b^2 c^2) (a^4-a^2 b^2-b^2 c^2+c^4) (a^8 b^4-2 a^6 b^6+a^4 b^8+3 a^8 b^2 c^2-3 a^6 b^4 c^2+a^4 b^6 c^2-a^2 b^8 c^2+a^8 c^4-3 a^6 b^2 c^4+a^4 b^4 c^4+a^2 b^6 c^4-b^8 c^4-2 a^6 c^6+a^4 b^2 c^6+a^2 b^4 c^6+2 b^6 c^6+a^4 c^8-a^2 b^2 c^8-b^4 c^8) : : , the X(6)-Ceva conjugate of X(98), on the lines {98,237}, {232,9468}, SEARCH = 0.727891386231371.

These points are now X(70602), X(70604) in ETC.

K1408 is the isogonal transform of K1404.