X3897

X2476com[INVERSE(n(4th EULER TRIANGLE))]

< 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) { 1, 21 }: Central Line L(1, 21) { 2, 355 }: Central Line L(2, 355) { 388, 1319 }: Central Line L(388, 1319) { 214, 1698 }: Central Line L(214, 1698) { 8, 2320 }: Central Line L(8, 2320) { 1001, 1388 }: Central Line L(1001, 1388) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1 = INCENTER (0.5714, 0.2333) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_2 = CENTROID (0.5374, 0.2000) X_355 = FUHRMANN CENTER (0.5408, 0.2645) X_388 = ∩X(7)X(8) (0.5790, 0.2635) X_1319 = BEVAN-SCHRÖDER POINT (0.9524, 0.9331) X_214 = -CEVA CONJUGATE OF X(44) (0.3571, 0.3499) X_1698 = INSIMILICENTER(BEVAN CIRCLE, NINE-POINTCIRCLE) (0.5306, 0.1933) X_8 = NAGEL POINT (0.4694, 0.1333) X_2320 = -ISOCONJUGATE OF X(1405) (0.5446, 0.1940) X_1001 = MIDPOINT OF X(1) AND X(9) (0.5412, 0.1974) X_1388 = POINT ANCHA (0.4835, 0.0718) X_3897 = com[INVERSE(n(4th EULER TRIANGLE))] (0.5368, 0.1877) A B C X1 X21 X2 X355 X388 X1319 X214 X1698 X8 X2320 X1001 X1388 X3897 (a, b, c) = (5, 6, 7) | AB = 1

X3897 (X2476com[INVERSE(n(4th EULER TRIANGLE))]) 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 \(f(a,b,c) = a(b + c - a)(b^{2} + c^{2} - 2a^{2} - ab - ac - 3bc)\)
Search Value (6, 9, 13): \(3.003898589275\)
▸ Incident Central Lines13 lines

{1, 21}, {2, 355}, {8, 2320}, {100, 3612}, {214, 1698}, {388, 1319}, {404, 3576}, {452, 3487}, {515, 2476}, {958, 3715}, {1001, 1388}, {1320, 1697}, {2136, 3601}