X1984

VEGA TRANSFORM OF X1020

X1984 = crosssum of X851 and X1020
< 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_1984 = VEGA TRANSFORM OF X(1020) (0.4361, -0.0651) A B C X2 X3 X4 X1984 (a, b, c) = (5, 6, 7) | AB = 1

X1984 (VEGA TRANSFORM OF X1020) 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 \(f(A,B,C) = (\cos^{2} A - \cos B \cos C)(\cos B - \cos C)^{2}/(\cos B + \cos C)\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(3.684876895025\)
▸ Incident Central Lines1 line

{2, 3}

▸ Functional Relations1 relation

Notes

As a point on the Euler line, X1984 has Shinagawa coefficients \((\$a(S_{A})^{3}\$ - \$a(S_{A})^{2}\$E + \$aS_{A}\$(E - F)F - 2abc(E - 2F)F, -\$a(S_{A})^{3}\$ + \$a(S_{A})^{2}\$E + \$aS_{B}S_{C}\$(E - 2F) - \$aS_{A}\$(E + F)F - 2abc[(E + F)F - S^{2}])\).