X1264

ISOTOMIC CONJUGATE OF X1118

X1264 is the isotomic conjugate of X1118.
< 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) { 69, 72 }: Central Line L(69, 72) { 8, 314 }: Central Line L(8, 314) { 219, 332 }: Central Line L(219, 332) { 319, 341 }: Central Line L(319, 341) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1118 = 1st HATZIPOLAKIS PERSPECTOR (0.6247, 0.5521) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.4122, 0.0654) X_72 = ISOGONAL CONJUGATE OF X(28) (0.4367, 0.0733) X_8 = NAGEL POINT (0.4694, 0.1333) X_314 = ISOTOMIC CONJUGATE OF X(65) (0.4457, 0.1206) X_219 = -CEVA CONJUGATE OF X(55) (0.4277, 0.0625) X_332 = ISOTOMIC CONJUGATE OF X(225) (0.3595, 0.0434) X_319 = ISOTOMIC CONJUGATE OF X(79) (0.4549, 0.1161) X_341 = ISOTOMIC CONJUGATE OF X(269) (0.3509, 0.0650) X_1264 = ISOTOMIC CONJUGATE OF X(1118) (0.2370, 0.0091) A B C X1118 X69 X72 X8 X314 X219 X332 X319 X341 X1264 (a, b, c) = (5, 6, 7) | AB = 1

X1264 (ISOTOMIC CONJUGATE OF X1118) 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 X1118)
Search Value (6, 9, 13): \(6.480405418744\)
▸ Alternate Coordinates1 form

  • Trilinears: \(g(A,B,C) : g(B,C,A) : g(C,A,B)\), where \(g(A, B, C) = (\cot^{2} A)/(1 - \cos A)\)

▸ Incident Central Lines4 lines

{8, 314}, {69, 72}, {219, 332}, {319, 341}

▸ Functional Relations2 relations