X2119

X2-ISOCONJUGATE OF X2118

< 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, 2118 }: Central Line L(238, 2118) { 365, 2110 }: Central Line L(365, 2110) { 1, 2146 }: Central Line L(1, 2146) 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_2118 = POINT KEPLER VII (1.6762, 1.6136) X_365 = SQUARE ROOT POINT (0.5864, 0.2502) X_2110 = POINT KEPLER III (-0.2477, 0.7305) X_1 = INCENTER (0.5714, 0.2333) X_2146 = -CEVA CONJUGATE OF X(365) (-0.3206, 0.6940) X_2119 = -ISOCONJUGATE OF X(2118) (1.0031, 0.0103) A B C X238 X2118 X365 X2110 X1 X2146 X2119 (a, b, c) = (5, 6, 7) | AB = 1

X2119 (X2-ISOCONJUGATE OF X2118) 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 \(f(a,b,c) = a^{1/2}/[(a + b + c)(abc)^{1/2} + (bc + ca + ab)[a^{1/2} - b^{1/2} - c^{1/2})]\) (M. Iliev, 5/13/07)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(0.300280734599\)
▸ Incident Central Lines3 lines

{1, 2146}, {238, 2118}, {365, 2110}