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X(1), X(6), X(8), X(37), X(188), X(312), X(333), X(1999), X(3210), X(17778), X(56279), X(71175), X(71176), X(71177), X(71178)

vertices of the cevian triangle of X(1999)

vertices of the anticevian triangle of X(188)

Geometric properties :

K1432 is a member of the pencil of pKs with pole X(9), pivot on the line {1,2} and isopivot on the Feuerbach hyperbola.

The isopivot of K1432 is X(71175) = a (a-b-c) (-a b^2-b^3+a^2 c-a b c-b^2 c+a c^2) (a^2 b+a b^2-a b c-a c^2-b c^2-c^3) : : , on the Feuerbach hyperbola and on the lines {X1, X2092}, {X4, X740}, {X6, X987}, {X7, X3210}, {X21, X2269}, {X42, X2298}, {X84, X511}, etc, SEARCH = 19.4749004576560.

This pencil contains K157, K199, K201, K1077, K1429 with pivots X(1), X(8), X(145), X(2), X(10) respectively.