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X(3), X(6), X(24), X(25), X(1609), X(2351), X(9937), X(34428), X(60775), X(60776)

vertices of the cevian triangle of X(24)

vertices of the anticevian triangle KaKbKc of X(6)

points of pK(X6, X6515) on (O)

infinite points of pK(X6, P) with P on the lines {25,110}, {66,69}

Geometric properties :

K1358 is related to the cubics K621, K1357 and to the quartic Q187.

The polar conic (C) of the pivot X(24) is a diagonal conic in ABC and a circum-conic in KaKbKc. It passes through H, K, X(24).

K1358 is also a pK in KaKbKc with pivot X(6) and isopivot X(24).

The isogonal transform of K1358 is pK(X2, X317).

Points on K1358 :

• X(60775) : isogonal conjugate of X(6515), barycentric quotient X(32) ÷ X(1609), on the lines {X3, X2165}, {X6, X1147}, {X24, X254}, {X25, X571}, {X37, X921}, {X159, X1976}, SEARCH = 6.33965615590575.

• X(60776) : X(24)-Ceva conjugate of X(6), on the lines {X3, X49}, {X6, X2351}, {X25, X571}, {X50, X161}, {X154, X3135}, SEARCH = 1.93260261897217.