X1267

ISOTOMIC CONJUGATE OF X1123

X1267 is the isotomic conjugate of X1123.
< 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, 37 }: Central Line L(2, 37) { 7, 492 }: Central Line L(7, 492) { 8, 491 }: Central Line L(8, 491) { 319, 1271 }: Central Line L(319, 1271) { 320, 1270 }: Central Line L(320, 1270) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1123 = PAASCHE POINT (0.5572, 0.2178) X_2 = CENTROID (0.5374, 0.2000) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_7 = GERGONNE POINT (0.5903, 0.2769) X_492 = CEVAPOINT OF X(2) AND X(488) (0.4893, 0.1483) X_8 = NAGEL POINT (0.4694, 0.1333) X_491 = CEVAPOINT OF X(2) AND X(487) (0.7449, 0.4229) X_319 = ISOTOMIC CONJUGATE OF X(79) (0.4549, 0.1161) X_1271 = ISOTOMIC CONJUGATE OF X(1132) (-0.0936, -0.4782) X_320 = ISOTOMIC CONJUGATE OF X(80) (-2.6735, -3.5993) X_1270 = ISOTOMIC CONJUGATE OF X(1131) (0.4679, 0.1253) X_1267 = ISOTOMIC CONJUGATE OF X(1123) (0.5162, 0.1825) A B C X1123 X2 X37 X7 X492 X8 X491 X319 X1271 X320 X1270 X1267 (a, b, c) = (5, 6, 7) | AB = 1

X1267 (ISOTOMIC CONJUGATE OF X1123) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(1/(a^{2}f(a,b,c)) : 1/(b^{2}f(b,c,a)) : 1/(c^{2}f(c,a,b))\), where f(a,b,c) is as in X1123)
Search Value (6, 9, 13): \(3.315315796423\)
▸ Alternate Coordinates2 forms

  • Trilinears: \(g(A,B,C) : g(B,C,A) : g(C,A,B)\), where \(g(A, B, C) = (\csc A)(1 + \csc A)\)

  • Trilinears: \((bc + S)/a : (ca + S)/b : (ab + S)/c\)

▸ Incident Central Lines5 lines

{2, 37}, {7, 492}, {8, 491}, {319, 1271}, {320, 1270}

▸ Functional Relations2 relations