X2115

X2-ISOCONJUGATE OF X2114

< 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, 241 }: Central Line L(238, 241) { 672, 2112 }: Central Line L(672, 2112) { 1931, 2116 }: Central Line L(1931, 2116) 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_241 = -LINE CONJUGATE OF X(55) (1.1217, 1.2442) X_672 = CROSSDIFFERENCE OF X(1) AND X(514) (1.9245, 2.2184) X_2112 = POINT KEPLER IV (-0.0981, 0.7800) X_1931 = CROSSDIFFERENCE OF PU(32) (1.7418, 1.7715) X_2116 = POINT KEPLER VI (0.0488, 0.8023) X_2115 = -ISOCONJUGATE OF X(2114) (-0.5439, 0.4629) A B C X238 X241 X672 X2112 X1931 X2116 X2115 (a, b, c) = (5, 6, 7) | AB = 1

X2115 (X2-ISOCONJUGATE OF X2114) 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 \(f(a,b,c) = (b + c - a)a/[a^{4} + (b + c)a^{3} - u(a,b,c)a^{2} + v(a,b,c)a - w(a,b,c)]\), where \(u(a,b,c) = 2b^{2} + 3bc + 2c^{2}\), \(v(a,b,c) = (b + c)(b^{2} + c^{2})\), \(w(a,b,c) = (b - c)^{2}(b^{2} + bc + c^{2})\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(10.436589607618\)
▸ Incident Central Lines3 lines

{238, 241}, {672, 2112}, {1931, 2116}