X607

ISOGONAL CONJUGATE OF X348

X607 is the isogonal conjugate of X348.
< 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, 19 }: Central Line L(6, 19) { 8, 29 }: Central Line L(8, 29) { 25, 41 }: Central Line L(25, 41) { 4, 218 }: Central Line L(4, 218) { 33, 210 }: Central Line L(33, 210) { 92, 239 }: Central Line L(92, 239) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_348 = ISOTOMIC CONJUGATE OF X(281) (0.4854, 0.1069) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_19 = CLAWSON POINT (0.6246, 0.4244) X_8 = NAGEL POINT (0.4694, 0.1333) X_29 = CEVAPOINT OF INCENTER AND ORTHOCENTER (0.5903, 0.3384) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_41 = -CEVA CONJUGATE OF X(31) (0.5823, 0.2244) X_4 = ORTHOCENTER (0.6122, 0.3958) X_218 = -CEVA CONJUGATE OF X(55) (0.6557, 0.3333) X_33 = PERSPECTOR OF THE ORTHIC AND INTANGENTS TRIANGLES (0.6019, 0.3546) X_210 = -CEVA CONJUGATE OF X(37) (0.4925, 0.1466) X_92 = CEVAPOINT OF INCENTER AND CLAWSON POINT (0.5949, 0.3639) X_239 = -LINE CONJUGATE OF X(42) (4.2109, 3.7992) X_607 = ISOGONAL CONJUGATE OF X(348) (0.6187, 0.3865) A B C X348 X6 X19 X8 X29 X25 X41 X4 X218 X33 X210 X92 X239 X607 (a, b, c) = (5, 6, 7) | AB = 1

X607 (ISOGONAL CONJUGATE OF X348) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(a(1 + \sec A) : b(1 + \sec B) : c(1 + \sec c)\)
Barycentrics: \(a^{2}(1 + \sec A) : :\)
Search Value (6, 9, 13): \(7.794688847595\)
▸ Alternate Coordinates1 form

  • Trilinears: \(\sin A + \tan A : :\)

▸ Incident Central Lines13 lines

{1, 949}, {4, 218}, {6, 19}, {8, 29}, {9, 1039}, {25, 41}, {28, 1002}, {33, 210}, {56, 911}, {92, 239}, {213, 1096}, {227, 910}, {240, 611}

▸ Functional Relations7 relations

Notes

X607 is the {X6,X19}-harmonic conjugate of X608.