X1426

X225-BETH CONJUGATE OF X225

X1426 = X34-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) { 4, 7 }: Central Line L(4, 7) { 25, 34 }: Central Line L(25, 34) { 65, 225 }: Central Line L(65, 225) { 227, 228 }: Central Line L(227, 228) { 226, 429 }: Central Line L(226, 429) { 72, 860 }: Central Line L(72, 860) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_225 = -CEVA CONJUGATE OF X(65) (0.6246, 0.4451) X_4 = ORTHOCENTER (0.6122, 0.3958) X_7 = GERGONNE POINT (0.5903, 0.2769) 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_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_227 = -CEVA CONJUGATE OF X(65) (0.4792, -0.0460) X_228 = -CEVA CONJUGATE OF X(71) (0.5231, 0.1126) X_226 = -CEVA CONJUGATE OF X(65) (0.5778, 0.2588) X_429 = EULER X(58)-5th-SUBSTITUTION POINT (0.6024, 0.3700) X_72 = ISOGONAL CONJUGATE OF X(28) (0.4367, 0.0733) X_860 = INTERCEPT OF EULER LINE AND TRILINEAR POLAR OF X(92) (0.7856, 0.8494) X_1426 = -BETH CONJUGATE OF X(225) (0.6336, 0.5112) A B C X225 X4 X7 X25 X34 X65 X227 X228 X226 X429 X72 X860 X1426 (a, b, c) = (5, 6, 7) | AB = 1

X1426 (X225-BETH CONJUGATE OF X225) 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 \(u : v : w\) = X225
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-0.020629646155\)
▸ Incident Central Lines9 lines

{4, 7}, {25, 34}, {65, 225}, {72, 860}, {226, 429}, {227, 228}, {278, 959}, {517, 1068}, {1254, 1400}

▸ Functional Relations4 relations