X2361

X2-ISOCONJUGATE OF X2006

< 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, 31 }: Central Line L(6, 31) { 3, 47 }: Central Line L(3, 47) { 11, 238 }: Central Line L(11, 238) { 56, 255 }: Central Line L(56, 255) { 162, 243 }: Central Line L(162, 243) { 46, 582 }: Central Line L(46, 582) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_47 = -BETH CONJUGATE OF X(34) (0.7279, 0.4389) X_11 = FEUERBACH POINT (0.7347, 0.0667) X_238 = -LINE CONJUGATE OF X(37) (1.6190, 1.4775) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_255 = ISOGONAL CONJUGATE OF X(158) (0.4217, 0.0365) X_162 = CEVAPOINT OF X(108) AND X(109) (0.4897, 0.6018) X_243 = -LINE CONJUGATE OF X(73) (0.7516, 0.9505) X_46 = -CEVA CONJUGATE OF X(1) (0.6917, 0.4543) X_582 = HARMONIC OF X(500) (0.8750, 0.7214) X_2361 = -ISOCONJUGATE OF X(2006) (4.0000, 5.2758) A B C X6 X31 X3 X47 X11 X238 X56 X255 X162 X243 X46 X582 X2361 (a, b, c) = (5, 6, 7) | AB = 1

X2361 (X2-ISOCONJUGATE OF X2006) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(a/f(a,b,c) : b/f(b,c,a) : c/f(c,a,b)\), where f(a,b,c) is as in X2006
Search Value (6, 9, 13): \(12.911339777405\)
▸ Alternate Coordinates3 forms

  • Trilinears: \(\cos(A/2) \cos(3A/2) : \cos(B/2) \cos(3B/2) : \cos(C/2) \cos(3C/2)\) (M. Iliev, 4/12/07)

  • Trilinears: \(\cos A + \cos 2A : \cos B + \cos 2B : \cos C + \cos 2C\) (M. Iliev, 4/12/07)

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

▸ Incident Central Lines26 lines

{3, 47}, {6, 31}, {11, 238}, {36, 1464}, {44, 2342}, {46, 582}, {56, 255}, {65, 580}, {109, 1155}, {162, 243}, {228, 2148}, {283, 2148}, {283, 960}, {484, 1718}, {517, 1411}, {518, 1331}, {652, 663}, {920, 1062}, {1040, 1707}, {1110, 2149}, {1397, 2352}, {1724, 1837}, {1754, 1836}, {1780, 1858}, {1859, 2299}, {2150, 2193}

▸ Functional Relations3 relations