X3785

X2548com[INVERSE(nT(a², a² + b²))]

X3785 = anticomplement of X2548
< A B C >: Reference Triangle △ABC < K_a K_b K_c >: Anticomplementary Triangle △K_a K_b K_c [ A B ]: Sideline AB (Base c = 1) [ B C ]: Sideline BC (Side a) [ C A ]: Sideline CA (Side b) { 2, 2548 }: Central Line L(2, 2548) { 2, 32 }: Central Line L(2, 32) { 3, 69 }: Central Line L(3, 69) { 20, 76 }: Central Line L(20, 76) { 4, 183 }: Central Line L(4, 183) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) K_a = Anticomplementary Vertex K_a (1.6122, 0.5999) K_b = Anticomplementary Vertex K_b (-0.3878, 0.5999) K_c = Anticomplementary Vertex K_c (0.3878, -0.5999) X_2 = CENTROID (0.5374, 0.2000) X_2548 = INSIMILICENTER(MOSES CIRCLE, (X(4),2R)) (0.5840, 0.2606) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.4122, 0.0654) X_20 = DE LONGCHAMPS POINT (0.3878, -0.1916) X_76 = 3rd BROCARD POINT (0.4567, 0.1388) X_4 = ORTHOCENTER (0.6122, 0.3958) X_183 = TRILINEAR PRODUCT X(75)X(182) (0.4700, 0.1275) X_3785 = com[INVERSE(nT(a2, a2 + b2))] (0.4441, 0.0788) A B C Ka Kb Kc X2 X2548 X32 X3 X69 X20 X76 X4 X183 X3785 (a, b, c) = (5, 6, 7) | AB = 1

X3785 (X2548com[INVERSE(nT(a², a² + b²))]) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Barycentrics: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = (b^{2} + c^{2} - a^{2})(b^{2} + c^{2} + 3a^{2})\)
Search Value (6, 9, 13): \(6.060447729456\)
▸ Incident Central Lines15 lines

{2, 32}, {3, 69}, {4, 183}, {20, 76}, {39, 193}, {99, 3522}, {140, 1007}, {141, 3053}, {187, 3620}, {217, 394}, {316, 3091}, {317, 3088}, {325, 631}, {376, 1975}, {1384, 3619}

▸ Functional Relations2 relations