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∑ a^3 y z (c y - b z) = 0 ⟺ ∑ b c x^2 (c^2 y - b^2 z) = 0

X(1), X(6), X(55), X(57), X(365), X(1419), X(2067), X(6502), X(7133), X(42013)

vertices of the incentral triangle

Geometric properties :

The anticevian triangle of P is perspective to the circumcevian triangle of X(55) if and only if P lies on K1403. The locus of the perspector is K1253. See also CL072.

K1403 meets the circumcircle at A, B, C (where the tangents are the symmedians) and three points Q1, Q2, Q3. The tangents at these three points concur at X = a^2 (a^2+2 a b-3 b^2+2 a c-26 b c-3 c^2) : : , SEARCH = 1.95334956924379.

The inconic with perspector X(1) is also inscribed in Q1Q2Q3 and the six contacts lie on the cubic.

The isogonal transform of K1403 is K363.

The symbolic substitution SS{a → a^2} transforms K1403 into K346.