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K1425

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

X(3), X(6), X(219), X(222), X(394), X(1073), X(1433), X(1498), X(7078), X(15905)

isogonal conjugates of X(6523), X(40837), X(40838), X(40839)

vertices of the cevian triangle of X(394)

vertices of the anticevian triangle of X(3)

Geometric properties :

The isogonal transform of K879 = pK(X393, X2) is K1425 = pK(X577, X394). Recall that X(393), X(577) and X(394) are the barycentric squares of X(4), X(3) and X(63) respectively.

K1425 is also the barycentric products X(3) x K007, X(69) x K172, X(63) x K343, X(394) x K879.

K1425 meets the line at infinity at the same points as pK(X3, X12111), pK(X800, X6515), pK(X6509, X69), pK(X14379, X64).

K1425 meets the circumcircle at the same points as pK(X32, X1498).

A locus property :

The anticevian triangle of P is perspective to the circumcevian triangle of X(1498) if and only if P lies on K1425. The locus of the perspector is a (not very interesting) pK with same pole.