X462

EULER LINE INTERCEPT OF LINE X51X_397

< 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 { 51, 397 }: Central Line L(51, 397) { 184, 398 }: Central Line L(184, 398) 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_51 = CENTROID OF ORTHIC TRIANGLE (0.6093, 0.3186) X_397 = CROSSPOINT OF X(4) AND X(17) (0.6029, 0.2975) X_184 = INVERSE OF X(125) IN THE BROCARD CIRCLE (0.5788, 0.1496) X_398 = CROSSPOINT OF X(4) AND X(18) (0.5945, 0.2099) X_462 = EULER LINE INTERCEPT OF LINE X(51)X(397) (0.7090, 0.6489) A B C X2 X3 X4 X51 X397 X184 X398 X462 (a, b, c) = (5, 6, 7) | AB = 1

X462 (EULER LINE INTERCEPT OF LINE X51X_397) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(u \tan A : v \tan B : w \tan C\), where \(u : v : w\) = X395; e.g., \(u(A,B,C) = \cos(B - C) + 2 \cos(A + \pi /3)\)
Barycentrics: \(u \sin A \tan A : v \sin B \tan B : w \sin C \tan C\)
Search Value (6, 9, 13): \(0.331515903660\)
▸ Incident Central Lines3 lines

{2, 3}, {51, 397}, {184, 398}

Notes

As a point on the Euler line, X462 has Shinagawa coefficients \((3^{1/2}F, -3^{1/2}(E + F) + 2S)\).