X308

ISOTOMIC CONJUGATE OF X39

X308 is the isotomic conjugate of X39.
< 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) { 6, 76 }: Central Line L(6, 76) { 25, 183 }: Central Line L(25, 183) { 69, 263 }: Central Line L(69, 263) { 42, 313 }: Central Line L(42, 313) { 290, 311 }: Central Line L(290, 311) { 251, 385 }: Central Line L(251, 385) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_39 = BROCARD MIDPOINT (0.5778, 0.2305) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_76 = 3rd BROCARD POINT (0.4567, 0.1388) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_183 = TRILINEAR PRODUCT X(75)X(182) (0.4700, 0.1275) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.4122, 0.0654) X_263 = ISOGONAL CONJUGATE OF X(183) (0.6298, 0.3525) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_313 = ISOTOMIC CONJUGATE OF X(58) (0.4368, 0.1249) X_290 = ISOGONAL CONJUGATE OF X(237) (0.7829, -0.1380) X_311 = ISOTOMIC CONJUGATE OF X(54) (0.4818, 0.1803) X_251 = ISOGONAL CONJUGATE OF X(141) (0.6177, 0.3042) X_385 = -HIRST INVERSE OF X(6) (2.2863, 2.0795) X_308 = ISOTOMIC CONJUGATE OF X(39) (0.4915, 0.1700) A B C X39 X6 X76 X25 X183 X69 X263 X42 X313 X290 X311 X251 X385 X308 (a, b, c) = (5, 6, 7) | AB = 1

X308 (ISOTOMIC CONJUGATE OF X39) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(b^{3}c^{3}/(b^{2} + c^{2}) : :\)
Barycentrics: \((b^{2}c^{2})/(b^{2} + c^{2}) : :\)
Search Value (6, 9, 13): \(3.949638855499\)
▸ Alternate Coordinates4 forms

  • Trilinears: \(\csc^{2} A \csc(A + \omega ) : :\)

  • Trilinears: \([\csc(A - \omega )]/(b^{2} + c^{2}) : :\)

  • Trilinears: \(\csc(A + \omega ) + \csc(A - \omega ) : :\)

  • Barycentrics: \(\csc A \csc(A + \omega ) : :\)

▸ Incident Central Lines9 lines

{2, 702}, {6, 76}, {25, 183}, {42, 313}, {69, 263}, {111, 689}, {141, 670}, {251, 385}, {290, 311}

▸ Functional Relations11 relations