X1589

POINT CHARA I

< A B C >: Reference Triangle △ABC [ A B ]: Sideline AB (Base c = 1) [ B C ]: Sideline BC (Side a) [ C A ]: Sideline CA (Side b) { 2, 3 }: Euler Line { 343, 487 }: Central Line L(343, 487) { 394, 488 }: Central Line L(394, 488) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2 = CENTROID (0.5374, 0.2000) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_4 = ORTHOCENTER (0.6122, 0.3958) X_343 = ISOTOMIC CONJUGATE OF X(275) (0.4345, 0.0893) X_487 = ANTICOMPLEMENT OF X(486) (1.7742, 0.6338) X_394 = -CEVA CONJUGATE OF X(3) (0.3778, 0.0284) X_488 = ANTICOMPLEMENT OF X(485) (0.4576, 0.0844) X_1589 = POINT CHARA I (0.5063, 0.1185) A B C X2 X3 X4 X343 X487 X394 X488 X1589 (a, b, c) = (5, 6, 7) | AB = 1

X1589 (POINT CHARA I) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(f(A,B,C) : f(B,C,A) : f(C,A,B)\), where \(f(A,B,C) = \csc A + \sec B \sec C\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(-0.253774918394\)
▸ Incident Central Lines3 lines

{2, 3}, {343, 487}, {394, 488}

Notes

As a point on the Euler line, X1589 has Shinagawa coefficients \((F + S, -S)\).