X467

EULER LINE INTERCEPT OF LINE X53X_311

X467 = X317-Ceva conjugate of X52
< 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 { 53, 311 }: Central Line L(53, 311) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_317 = ISOTOMIC CONJUGATE OF X(68) (0.6796, 0.5070) X_52 = ORTHOCENTER OF ORTHIC TRIANGLE (0.7155, 0.4580) X_2 = CENTROID (0.5374, 0.2000) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_53 = SYMMEDIAN POINT OF ORTHIC TRIANGLE (0.6164, 0.4390) X_311 = ISOTOMIC CONJUGATE OF X(54) (0.4818, 0.1803) X_467 = EULER LINE INTERCEPT OF LINE X(53)X(311) (0.6632, 0.5291) A B C X317 X52 X2 X3 X53 X311 X467 (a, b, c) = (5, 6, 7) | AB = 1

X467 (EULER LINE INTERCEPT OF LINE X53X_311) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(u \csc 2A : v \csc 2B : w \csc 2C\), where \(u : v : w\) = X52; e.g., \(u(A,B,C) = \cos 2A \cos(B - C)\)
Barycentrics: \(u \sec A : v \sec B : w \sec C\)
Search Value (6, 9, 13): \(0.742978326523\)
▸ Incident Central Lines2 lines

{2, 3}, {53, 311}

▸ Functional Relations2 relations

Notes

As a point on the Euler line, X467 has Shinagawa coefficients \(((E + 2F)F,-2S^{2})\).