X2400

GIBERT-SIMSON TRANSFORM OF X103

X2400 = X676-cross conjugate of X514
< 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) { 7, 522 }: Central Line L(7, 522) { 103, 675 }: Central Line L(103, 675) { 677, 883 }: Central Line L(677, 883) { 673, 918 }: Central Line L(673, 918) { 693, 1088 }: Central Line L(693, 1088) { 86, 2424 }: Central Line L(86, 2424) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2426 = ISOGONAL CONJUGATE OF X(2400) (0.9279, 0.7503) X_7 = GERGONNE POINT (0.5903, 0.2769) X_522 = ISOGONAL CONJUGATE OF X(109) (-0.0318, 0.3430) X_103 = ANTIPODE OF X(101) (0.7857, -0.3208) X_675 = TRILINEAR POLE OF LINE X(6)X(514) (0.9212, -0.1860) X_677 = TRILINEAR POLE OF LINE X(3)X(101) (1.3200, 0.4790) X_883 = INTERSECTION OF LINES X(7)X(8) AND X(190)X(644) (1.5694, 1.4397) X_673 = TRILINEAR POLE OF LINE X(1)X(514) (0.9471, -0.0769) X_918 = ISOTOMIC CONJUGATE OF X(666) (1.0192, 0.5351) X_693 = ISOTOMIC CONJUGATE OF X(100) (-25.8163, 8.9981) X_1088 = TRILINEAR SQUARE OF X(7) (0.6052, 0.3210) X_86 = CEVAPOINT OF INCENTER AND CENTROID (0.5534, 0.2171) X_2424 = ISOGONAL CONJUGATE OF X(2398) (1.0916, 0.1371) X_2400 = GIBERT-SIMSON TRANSFORM OF X(103) (1.2261, 0.1171) A B C X2426 X7 X522 X103 X675 X677 X883 X673 X918 X693 X1088 X86 X2424 X2400 (a, b, c) = (5, 6, 7) | AB = 1

X2400 (GIBERT-SIMSON TRANSFORM OF X103) 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 as given just before X2394
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-14.581409817390\)

X2400 lies on the cubic K010.

▸ Incident Central Lines7 lines

{2, 3239}, {7, 522}, {86, 2424}, {103, 675}, {673, 918}, {677, 883}, {693, 1088}

▸ Functional Relations5 relations