X1053

POINT ALHENA

< 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) { 238, 517 }: Central Line L(238, 517) { 1, 1110 }: Central Line L(1, 1110) { 905, 1054 }: Central Line L(905, 1054) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_238 = -LINE CONJUGATE OF X(37) (1.6190, 1.4775) X_517 = ISOGONAL CONJUGATE OF X(104) (0.8180, 0.7154) X_1 = INCENTER (0.5714, 0.2333) X_1110 = TRILINEAR SQUARE OF X(101) (0.5057, 0.3942) X_905 = POINT ACHERNAR (5.6190, -0.6999) X_1054 = 6th SHARYGIN POINT (1.4286, -0.2333) X_1053 = POINT ALHENA (0.7302, -0.1555) A B C X238 X517 X1 X1110 X905 X1054 X1053 (a, b, c) = (5, 6, 7) | AB = 1

X1053 (POINT ALHENA) 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 \(f(a,b,c) = -u^{2} + v^{2} + w^{2} + vw + wu + uv\),\(u : v : w\) = X101
Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = af(a,b,c)\)
Search Value (6, 9, 13): \(13.097051131220\)
▸ Incident Central Lines3 lines

{1, 1110}, {238, 517}, {905, 1054}