X448

X2-HIRST INVERSE OF X21

X448 is the X2-hirst inverse of X21.
< 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_448 = -HIRST INVERSE OF X(21) (-2.0878, -6.6689) A B C X2 X3 X4 X448 (a, b, c) = (5, 6, 7) | AB = 1

X448 (X2-HIRST INVERSE OF X21) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(bc(u^{2} - vw) : ca(v^{2} - wu) : ab(w^{2} - uv)\), where \(u : v : w\) = X284; e.g., \(u(A,B,C) = (\sin A)/(\cos B + \cos C)\)
Barycentrics: \(u^{2} - vw : v^{2} - wu : w^{2} - uv\)
Search Value (6, 9, 13): \(10.626943612527\)
▸ Incident Central Lines1 line

{2, 3}

▸ Functional Relations1 relation

Notes

As a point on the Euler line, X448 has Shinagawa coefficients \(((E-2F)S^{4}-2(E^{2}-F^{2})FS^{2} -\$abS_{A}S_{B}\$[4(E+F)F-3S^{2}] +\$ab\$[2(E+F)FS^{2}-S^{4}], -(E-4F)S^{4} -5\$abS_{A}S_{B}\$S^{2}+\$ab\$S^{4})\).