X1410

X73-BETH CONJUGATE OF X73

X1410 = X56-Ceva conjugate of X1042
< 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) { 25, 34 }: Central Line L(25, 34) { 3, 77 }: Central Line L(3, 77) { 73, 228 }: Central Line L(73, 228) { 32, 604 }: Central Line L(32, 604) { 184, 603 }: Central Line L(184, 603) { 98, 934 }: Central Line L(98, 934) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_73 = CROSSPOINT OF INCENTER AND CIRCUMCENTER (0.5487, 0.1428) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_34 = -BETH CONJUGATE OF X(4) (0.6332, 0.4792) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_77 = ISOGONAL CONJUGATE OF X(33) (0.5270, 0.1305) X_228 = -CEVA CONJUGATE OF X(71) (0.5231, 0.1126) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_604 = -CEVA CONJUGATE OF X(31) (0.6442, 0.3744) X_184 = INVERSE OF X(125) IN THE BROCARD CIRCLE (0.5788, 0.1496) X_603 = -CEVA CONJUGATE OF X(56) (0.5992, 0.1851) X_98 = TARRY POINT (0.8891, -0.2281) X_934 = -CROSS CONJUGATE OF X(57) (0.4269, 0.6071) X_1410 = -BETH CONJUGATE OF X(73) (0.6303, 0.2394) A B C X73 X25 X34 X3 X77 X228 X32 X604 X184 X603 X98 X934 X1410 (a, b, c) = (5, 6, 7) | AB = 1

X1410 (X73-BETH CONJUGATE OF X73) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = (1 - \cos A)u(a,b,c)\), where \(u : v : w\) = X73
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-0.076938438297\)
▸ Incident Central Lines8 lines

{3, 77}, {25, 34}, {32, 604}, {58, 1461}, {73, 228}, {98, 934}, {184, 603}, {1042, 1402}

▸ Functional Relations3 relations