X302

ISOTOMIC CONJUGATE OF 1st NAPOLEON POINT

X302 is the isotomic conjugate of 1st Napoleon point.
< 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) { 2, 6 }: Centroid–Symmedian Line { 18, 76 }: Central Line L(18, 76) { 14, 99 }: Central Line L(14, 99) { 264, 300 }: Central Line L(264, 300) { 16, 316 }: Central Line L(16, 316) { 301, 311 }: Central Line L(301, 311) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_301 = ISOTOMIC CONJUGATE OF 2nd ISODYNAMIC CENTER (0.8423, -0.0749) X_299 = ISOTOMIC CONJUGATE OF 2nd ISOGONIC CENTER (-1.1465, -1.6097) X_2 = CENTROID (0.5374, 0.2000) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_18 = 2nd NAPOLEON POINT (0.4434, 0.1317) X_76 = 3rd BROCARD POINT (0.4567, 0.1388) X_14 = 2nd ISOGONIC CENTER (0.9134, -0.1143) X_99 = STEINER POINT (0.1109, 0.4322) X_264 = ISOTOMIC CONJUGATE OF CIRCUMCENTER (0.5720, 0.3293) X_300 = ISOTOMIC CONJUGATE OF 1st ISODYNAMIC CENTER (0.5239, 0.2121) X_16 = 2nd ISODYNAMIC POINT (1.8453, 2.3239) X_316 = DROUSSENT PIVOT (-0.7850, -1.9118) X_311 = ISOTOMIC CONJUGATE OF X(54) (0.4818, 0.1803) X_302 = ISOTOMIC CONJUGATE OF 1st NAPOLEON POINT (0.5043, 0.1643) A B C X301 X299 X2 X6 X18 X76 X14 X99 X264 X300 X16 X316 X311 X302 (a, b, c) = (5, 6, 7) | AB = 1

X302 (ISOTOMIC CONJUGATE OF 1st NAPOLEON POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(\csc^{2} A \sin(A + \pi /6) : \csc^{2} B \sin(B + \pi /6) : \csc^{2} C \sin(C + \pi /6)\)
Barycentrics: \(\csc A \sin(A + \pi /6) : \csc B \sin(B + \pi /6) : \csc C \sin(C + \pi /6)\)
Search Value (6, 9, 13): \(3.832751081755\)
▸ Incident Central Lines13 lines

{2, 6}, {3, 621}, {5, 622}, {14, 99}, {16, 316}, {18, 76}, {61, 629}, {140, 633}, {264, 300}, {301, 311}, {317, 470}, {381, 616}, {549, 617}

▸ Functional Relations5 relations