X2418

GIBERT-SIMSON TRANSFORM OF X1296

X2418 = trilinear pole of line X126X524 (the Simson line of X1296)
< 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) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2444 = ISOGONAL CONJUGATE OF X(2418) (0.9861, 0.0334) X_2418 = GIBERT-SIMSON TRANSFORM OF X(1296) (-0.2483, -0.2273) A B C X2444 X2418 (a, b, c) = (5, 6, 7) | AB = 1

X2418 (GIBERT-SIMSON TRANSFORM OF X1296) 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 \(f(a,b,c) = bc(2a^{2} - b^{2} - c^{2})/[(5a^{2} - b^{2} - c^{2})(b^{2} - c^{2})]\) (M. Iliev, 5/13/07)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(6.117649895464\)

X2418 lies on the cubic K010 and these linea: 99,1296 2,5024

▸ Functional Relations3 relations