X3168

X6-CEVA CONJUGATE OF X4

X3168 = X6-Ceva conjugate of X4
< 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) { 4, 51 }: Central Line L(4, 51) { 107, 184 }: Central Line L(107, 184) { 6, 436 }: Central Line L(6, 436) { 262, 459 }: Central Line L(262, 459) { 232, 800 }: Central Line L(232, 800) { 2, 1972 }: Central Line L(2, 1972) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_4 = ORTHOCENTER (0.6122, 0.3958) X_51 = CENTROID OF ORTHIC TRIANGLE (0.6093, 0.3186) X_107 = Ψ(SYMMEDIAN POINT, ORTHOCENTER) (0.5733, 0.6071) X_184 = INVERSE OF X(125) IN THE BROCARD CIRCLE (0.5788, 0.1496) X_436 = EULER X(48)-7th-SUBSTITUTION POINT (0.6027, 0.3709) X_262 = ISOGONAL CONJUGATE OF X(182) (0.5893, 0.2856) X_459 = -CEVA CONJUGATE OF X(4) (0.5934, 0.8103) X_232 = -CEVA CONJUGATE OF X(132) (0.6919, 0.7779) X_800 = CROSSPOINT OF X(2) AND X(64) (0.6501, 0.3499) X_2 = CENTROID (0.5374, 0.2000) X_1972 = TRILINEAR POLE OF PU(38) (0.5839, -0.3149) X_3168 = -CEVA CONJUGATE OF X(4) (0.5844, -0.3207) A B C X6 X4 X51 X107 X184 X436 X262 X459 X232 X800 X2 X1972 X3168 (a, b, c) = (5, 6, 7) | AB = 1

X3168 (X6-CEVA CONJUGATE OF X4) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(u(-u/x + v/y + w/z) : v(u/x - v/y + w/z) : w(u/x + v/y - w/z)\), where \(x : y : z\) = X6 and \(u : v : w\) = X4
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\), where \(f(a,b,c) = u(-u/x + v/y + w/z)\)
Search Value (6, 9, 13): \(0.668144278146\)
▸ Incident Central Lines8 lines

{2, 1972}, {4, 51}, {6, 436}, {107, 184}, {232, 800}, {262, 459}, {450, 1993}, {1148, 1870}

▸ Functional Relations2 relations