X329

ISOTOMIC CONJUGATE OF X189

X329 is the isotomic conjugate of X189.
< 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, 7 }: Centroid–Gergonne Line { 4, 8 }: Fuhrmann Line { 20, 78 }: Central Line L(20, 78) { 69, 189 }: Central Line L(69, 189) { 1, 452 }: Central Line L(1, 452) { 100, 972 }: Central Line L(100, 972) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_189 = CYCLOCEVIAN CONJUGATE OF X(8) (0.6131, 0.7055) X_2 = CENTROID (0.5374, 0.2000) X_7 = GERGONNE POINT (0.5903, 0.2769) X_4 = ORTHOCENTER (0.6122, 0.3958) X_8 = NAGEL POINT (0.4694, 0.1333) X_20 = DE LONGCHAMPS POINT (0.3878, -0.1916) X_78 = ISOGONAL CONJUGATE OF X(34) (0.3835, 0.0491) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.4122, 0.0654) X_1 = INCENTER (0.5714, 0.2333) X_452 = -HIRST INVERSE OF X(449) (0.5268, 0.1722) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.1429, 0.4666) X_972 = ISOGONAL CONJUGATE OF X(971) (0.5731, -0.4030) X_329 = ISOTOMIC CONJUGATE OF X(189) (0.3847, -0.0222) A B C X189 X2 X7 X4 X8 X20 X78 X69 X1 X452 X100 X972 X329 (a, b, c) = (5, 6, 7) | AB = 1

X329 (ISOTOMIC CONJUGATE OF X189) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(( -1 - \cos A + \cos B + \cos C)(\csc A) : :\)
Barycentrics: \(-1 - \cos A + \cos B + \cos C : :\)
Search Value (6, 9, 13): \(7.127195794431\)
▸ Alternate Coordinates1 form

  • Barycentrics: \(a^{3} + a^{2}(b + c) - a(b + c)^{2} - (b - c)^{2}(b + c) : :\)

▸ Linear Combinations1 combination

X329 lies on the Lucas cubic.

▸ Incident Central Lines20 lines

{1, 452}, {2, 7}, {3, 2096}, {4, 8}, {5, 2095}, {6, 4415}, {10, 2093}, {11, 5825}, {20, 78}, {69, 189}, {75, 14555}, {100, 972}, {165, 6745}, {193, 1999}, {198, 1817}, {220, 948}, {440, 3161}, {971, 10430}, {5687, 6361}, {5817, 7956}

▸ Functional Relations15 relations