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∑ (b^2 + c^2) x^2 (c^2 SB y – b^2 SC z) = 0 

X(2), X(22), X(25), X(251), X(1799), X(8793), X(8879), X(8880), X(8881), X(13575) X(16277) = X(3313)* = isogonal conjugate of X(3313), on the Kiepert hyperbola A'B'C' = cevian triangle of X(1799) (yellow) circumcevian triangle of X(2) cevian triangle of X(251) wrt circumcevian triangle of X(2) cevian triangle of X(25) wrt cevian triangle of X(1799) other points below 

Geometric properties : 

K959 is the isogonal transform of K140, also the barycentric quotient of K140 by X(141). K959 meets the line at infinity at the same points as (K1) = pK(X2, P1) where P1 = X(16275) = X(2)X(187) /\ X(305)X(315). The six remaining common points are A, B, C, X(2), X(1799), X(13575) on the circumconic with perspector X(525). K959 meets the Steiner ellipse at the same points as (K2) = pK(X2, P2) where P2 = X(16276) = X(2)X(99) /\ X(22)X(76). The three remaining common points are those on the Euler line namely X(2), X(22), X(25). Note that the line P1P2 is parallel to the Euler line. X(25) is the isopivot of K959 whose polar conic is a remarkable circumhyperbola passing through X(i) for these i : 3, 25, 32, 98, 184, 228, 878, 1402, 1410, 1799, 2200, 2351, 2353, 3425, 3437, 3438, 3439, 3442, 3443, 3455, 3456, 3504, 6401, 6402, 8825, 8858, 8884, 10547, 14600, 14908. Its equation is ∑ a^4 (b^2  c^2) (a^2 + b^2 + c^2) y z = 0, that of the circumconic with perspector X(3049). Locus properties
