X332

ISOTOMIC CONJUGATE OF X225

X332 is the isotomic conjugate of X225.
< 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) { 3, 69 }: Central Line L(3, 69) { 1, 75 }: Central Line L(1, 75) { 99, 102 }: Central Line L(99, 102) { 261, 284 }: Central Line L(261, 284) { 219, 345 }: Central Line L(219, 345) { 21, 1036 }: Central Line L(21, 1036) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_225 = -CEVA CONJUGATE OF X(65) (0.6246, 0.4451) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.4122, 0.0654) X_1 = INCENTER (0.5714, 0.2333) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_99 = STEINER POINT (0.1109, 0.4322) X_102 = Λ(INCENTER, ORTHOCENTER) (0.6364, -0.3897) X_261 = ISOTOMIC CONJUGATE OF X(12) (0.5072, 0.1625) X_284 = -CROSS CONJUGATE OF X(21) (0.5646, 0.2088) X_219 = -CEVA CONJUGATE OF X(55) (0.4277, 0.0625) X_345 = ISOTOMIC CONJUGATE OF X(278) (0.3405, 0.0381) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_1036 = ISOGONAL CONJUGATE OF X(388) (0.5632, 0.2044) X_332 = ISOTOMIC CONJUGATE OF X(225) (0.3595, 0.0434) A B C X225 X3 X69 X1 X75 X99 X102 X261 X284 X219 X345 X21 X1036 X332 (a, b, c) = (5, 6, 7) | AB = 1

X332 (ISOTOMIC CONJUGATE OF X225) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \((\cot A \csc A)/(\cos B + \cos C) : (\cot B \csc B)/(\cos C + \cos A) : (\cot C \csc C)/(\cos A + \cos B)\)
Barycentrics: \((\cot A)/(\cos B + \cos C) : (\cot B)/(\cos C + \cos A) : (\cot C)/(\cos A + \cos B)\)
Search Value (6, 9, 13): \(5.737711191223\)
▸ Alternate Coordinates1 form

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

▸ Incident Central Lines7 lines

{1, 75}, {3, 69}, {21, 1036}, {99, 102}, {219, 345}, {261, 284}, {1014, 1037}

▸ Functional Relations5 relations