X3859

X632com(EULER TRIANGLE)

< 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 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_3859 = com(EULER TRIANGLE) (0.5730, 0.2930) A B C X2 X3 X4 X3859 (a, b, c) = (5, 6, 7) | AB = 1

X3859 (X632com(EULER TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Barycentrics: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = 6a^{4} - 13b^{4} - 13c^{4} + 7a^{2}b^{2} + 7a^{2}c^{2} + 26b^{2}c^{2}\)
Search Value (6, 9, 13): \(-1.315975604134\)
▸ Incident Central Lines1 line

{2, 3}

Notes

As a point on the Euler line, X3859 has Shinagawa coefficients \((7, 19)\)