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X(2), X(4), X(6), X(51), X(290), X(311), X(511), X(1976), X(11610), X(41334), X(44176), X(53174), X(53245)

X(60517) = X(5) x X(98) = X(51) x X(290), on the lines {X2,X290}, {X4,X32}, {X5,X217}, SEARCH = -0.249009163063951

X(60514) → X(60523), X(60592), X(60593), X(60594)

cevians of X(290)

infinite points of the circum-conic with perspector X(51)

Geometric properties :

K1354 is an example of cubic pK(Ω, P) which passes through the centers X(2), X(4), X(6). See K1352 for further details.

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Other centers on K1354

P1 = a^2 (a^2 b^2-b^4+a^2 c^2+2 b^2 c^2-c^4) (a^8-a^6 b^2-a^4 b^4+a^2 b^6-a^6 c^2-a^4 b^2 c^2+a^2 b^4 c^2+b^6 c^2-a^4 c^4+a^2 b^2 c^4-2 b^4 c^4+a^2 c^6+b^2 c^6) : : , SEARCH = 0.410753594565091

P2 = (a^2 b^2-b^4+a^2 c^2+2 b^2 c^2-c^4) (a^6-2 a^4 b^2+a^2 b^4-2 a^4 c^2-a^2 b^2 c^2+b^4 c^2+a^2 c^4+b^2 c^4) : : , SEARCH = -4.10969609355935

P3 = b^2 c^2 (a^4-2 a^2 b^2+b^4-2 b^2 c^2+c^4) (a^4+b^4-2 a^2 c^2-2 b^2 c^2+c^4) (2 a^4-a^2 b^2+b^4-a^2 c^2-2 b^2 c^2+c^4) : : , SEARCH = -0.893051108424639

P4 = (a^2 b^2-b^4+a^2 c^2+2 b^2 c^2-c^4) (a^8+a^6 b^2-a^4 b^4-a^2 b^6+a^6 c^2-a^4 b^2 c^2+a^2 b^4 c^2-b^6 c^2-a^4 c^4+a^2 b^2 c^4+2 b^4 c^4-a^2 c^6-b^2 c^6) : : , SEARCH = -0.121044927607571

P5 = b^2 c^2 (-a^2+b^2-c^2) (a^2+b^2-c^2) (-2 a^6+a^4 b^2+b^6+a^4 c^2-b^4 c^2-b^2 c^4+c^6) : : , SEARCH = 1.62924082862474

P6 = a^2 (a^6 b^2-a^2 b^6+a^6 c^2-b^6 c^2+2 b^4 c^4-a^2 c^6-b^2 c^6) : : , SEARCH = -2.28332557171032