X317

ISOTOMIC CONJUGATE OF X68

X317 is the isotomic conjugate of X68.
< 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) { 4, 69 }: Central Line L(4, 69) { 2, 95 }: Central Line L(2, 95) { 6, 297 }: Central Line L(6, 297) { 66, 290 }: Central Line L(66, 290) { 25, 325 }: Central Line L(25, 325) { 53, 524 }: Central Line L(53, 524) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_68 = PRASOLOV POINT (-0.0535, -0.0055) X_4 = ORTHOCENTER (0.6122, 0.3958) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.4122, 0.0654) X_2 = CENTROID (0.5374, 0.2000) X_95 = CEVAPOINT OF CENTROID AND CIRCUMCENTER (0.5172, 0.1562) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_297 = -HIRST INVERSE OF X(4) (0.8440, 1.0022) X_66 = ISOGONAL CONJUGATE OF X(22) (0.5912, 1.0593) X_290 = ISOGONAL CONJUGATE OF X(237) (0.7829, -0.1380) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_325 = -HIRST INVERSE OF X(69) (-0.3370, -0.7398) X_53 = SYMMEDIAN POINT OF ORTHIC TRIANGLE (0.6164, 0.4390) X_524 = ISOGONAL CONJUGATE OF X(111) (0.1376, -0.2297) X_317 = ISOTOMIC CONJUGATE OF X(68) (0.6796, 0.5070) A B C X68 X4 X69 X2 X95 X6 X297 X66 X290 X25 X325 X53 X524 X317 (a, b, c) = (5, 6, 7) | AB = 1

X317 (ISOTOMIC CONJUGATE OF X68) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(\sec A \cos 2A \csc^{2} A : :\)
Barycentrics: \(\cot 2A : \cot 2B : \cot 2C\)
Search Value (6, 9, 13): \(3.944983833327\)
▸ Alternate Coordinates6 forms

  • Trilinears: \(bc \cot 2A : ca \cot 2B : ab \cot 2C\)

  • Trilinears: \(\sec A - \cot A \csc A : :\)

  • Barycentrics: \(\tan A \cos 2A \csc^{2} A\)

  • Barycentrics: \(\tan A - \cot A : :\)

  • Barycentrics: \(\tan A + \cot B + \cot C - \cot \omega : :\)

  • Barycentrics: \((a^{4} + b^{4} + c^{4} - 2 a^{2} b^{2} - 2 a^{2} c^{2}) / (b^{2} + c^{2} - a^{2}) : :\)

▸ Incident Central Lines17 lines

{2, 95}, {4, 69}, {6, 297}, {25, 325}, {53, 524}, {66, 290}, {141, 458}, {183, 427}, {193, 393}, {261, 406}, {273, 320}, {298, 473}, {299, 472}, {302, 470}, {303, 471}, {318, 319}, {1007, 6353}

▸ Functional Relations6 relations