X2061

ORION TRANSFORM OF X40

< 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) { 1, 3 }: OI Line (Incenter–Circumcenter Line) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1 = INCENTER (0.5714, 0.2333) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_2061 = ORION TRANSFORM OF X(40) (0.4602, 0.0290) A B C X1 X3 X2061 (a, b, c) = (5, 6, 7) | AB = 1

X2061 (ORION TRANSFORM OF X40) 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) is given just above X2055, using X = X40
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(7.776848115337\)
▸ Linear Combinations1 combination

  • X2061 = \(R(4R^{2} - s^{2} - S)(4R^{2} - s^{2} + S)\) X1 + \(2(4rR + 4R^{2} - s^{2})(4R^{3} + rs^{2} - R_{s}^{2})\) X3 (Peter Moses, April 2, 2012)

▸ Incident Central Lines1 line

{1, 3}