X1265

ISOTOMIC CONJUGATE OF X1119

X1265 is the isotomic conjugate of X1119.
< 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) { 20, 190 }: Central Line L(20, 190) { 8, 210 }: Central Line L(8, 210) { 1, 344 }: Central Line L(1, 344) { 78, 345 }: Central Line L(78, 345) { 220, 346 }: Central Line L(220, 346) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1119 = 2nd HATZIPOLAKIS PERSPECTOR (0.6322, 0.5039) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.4122, 0.0654) X_72 = ISOGONAL CONJUGATE OF X(28) (0.4367, 0.0733) X_20 = DE LONGCHAMPS POINT (0.3878, -0.1916) X_190 = YFF PARABOLIC POINT (0.0748, 0.3999) X_8 = NAGEL POINT (0.4694, 0.1333) X_210 = -CEVA CONJUGATE OF X(37) (0.4925, 0.1466) X_1 = INCENTER (0.5714, 0.2333) X_344 = ISOTOMIC CONJUGATE OF X(277) (0.6218, 0.2693) X_78 = ISOGONAL CONJUGATE OF X(34) (0.3835, 0.0491) X_345 = ISOTOMIC CONJUGATE OF X(278) (0.3405, 0.0381) X_220 = -CEVA CONJUGATE OF X(55) (0.4826, 0.1278) X_346 = ISOTOMIC CONJUGATE OF X(279) (0.3948, 0.0827) X_1265 = ISOTOMIC CONJUGATE OF X(1119) (0.2751, 0.0213) A B C X1119 X69 X72 X20 X190 X8 X210 X1 X344 X78 X345 X220 X346 X1265 (a, b, c) = (5, 6, 7) | AB = 1

X1265 (ISOTOMIC CONJUGATE OF X1119) 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 X1119)
Search Value (6, 9, 13): \(6.452192125285\)
▸ Alternate Coordinates1 form

  • Trilinears: \(g(A,B,C) : g(B,C,A) : g(C,A,B)\), where \(g(A, B, C) = (\cos A)(\csc^{4} A/2)\)

▸ Incident Central Lines8 lines

{1, 344}, {2, 1257}, {8, 210}, {20, 190}, {69, 72}, {78, 345}, {145, 1191}, {220, 346}

▸ Functional Relations3 relations