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X(1), X(9), X(44), X(57), X(88), X(104), X(517), X(2161), X(3218)

excenters

infinite points of the Mandart circum-ellipse

K717 is an isogonal pK related to K716. These two cubics share nine identified points namely A, B, C, X(9), X(57), X(517), X(2161) and the infinite points of the Mandart circum-ellipse hence they generate a pencil of cubics all passing through these same nine points which contains :

• one pK namely K717,

• two psKs namely :

– psK(X2161, tX3218, X4) with pseudo-pivot the isotomic conjugate of X(3218) and pseudo-isopivot X(6), passing through X(4), X(9), X(35), X(57), X(80), X(321), X(517), X(2161),

– psK(X2183, X2, X3), passing through X(3), X(9), X(57), X(517), X(908), X(1145), X(2161),

• a cubic decomposed into the line at infinity and the circum-conic with perspector X(663).

See also the very similar K1055 = pK(X6, X3219).