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X(1), X(4), X(8), X(85), X(169), X(277), X(279), X(2082), X(3673), X(6554), X(7195), X(14256), X(17170)

vertices of the cevian triangle of X(85)

infinite points of pK(X1418, X279)

other points below

Geometric properties :

K1189 is the image of K1188 under the symbolic substitution SS{a->√a}.

 

Centers on K1189

Q1 = (a^2-2 a b+b^2-2 a c+c^2) (a^2+b^2-2 b c+c^2) : : , SEARCH = -0.3661146419921

Q2 = (a+b-c) (a-b+c) (a^2+b^2-2 b c+c^2) (a^3-a^2 b+a b^2-b^3-a^2 c+2 a b c-b^2 c+a c^2-b c^2-c^3) : : , SEARCH = -1.814699262352962

Q3 = b c (a^2+b^2-2 b c+c^2) (-3 a^3+3 a^2 b-a b^2+b^3+3 a^2 c-2 a b c-b^2 c-a c^2-b c^2+c^3) : : , SEARCH = 1.887718894555595

Q4 = b c (a^2+b^2-2 b c+c^2) (a^3-a^2 b-a b^2+b^3-a^2 c-b^2 c+a c^2+b c^2-c^3) (-a^3+a^2 b-a b^2+b^3+a^2 c-b^2 c+a c^2+b c^2-c^3) : : , SEARCH = 0.7152170564976766

Q5 = (a-b-c) (a^2+b^2-2 b c+c^2) (a^4-2 a^3 b+2 a^2 b^2-2 a b^3+b^4-2 a^3 c+4 a^2 b c-2 b^3 c+2 a^2 c^2+2 b^2 c^2-2 a c^3-2 b c^3+c^4) : : , SEARCH = -4.301903868296176

Q6 = a (a^3-a^2 b-a b^2+b^3-a^2 c-2 a b c-b^2 c+3 a c^2+3 b c^2-3 c^3) (a^3-a^2 b+3 a b^2-3 b^3-a^2 c-2 a b c+3 b^2 c-a c^2-b c^2+c^3) : : , SEARCH = -0.8735000458847319

Q7 = (a-b-c) (a^3+a^2 b+a b^2+b^3-a^2 c-2 a b c-b^2 c+a c^2+b c^2-c^3) (a^3-a^2 b+a b^2-b^3+a^2 c-2 a b c+b^2 c+a c^2-b c^2+c^3) : : , SEARCH = 4.184572714156113

These points are now X(41785) -> X(41791) in ETC.