X1068

X46-CROSS CONJUGATE OF X4

X1068 = isogonal conjugate of X1069
< 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) { 1, 4 }: Incenter–Orthocenter Line { 24, 108 }: Central Line L(24, 108) { 92, 406 }: Central Line L(92, 406) { 281, 451 }: Central Line L(281, 451) { 318, 475 }: Central Line L(318, 475) { 155, 651 }: Central Line L(155, 651) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_46 = -CEVA CONJUGATE OF X(1) (0.6917, 0.4543) X_4 = ORTHOCENTER (0.6122, 0.3958) X_1 = INCENTER (0.5714, 0.2333) X_24 = PERSPECTOR OF ABC AND ORTHIC-OF-ORTHIC TRIANGLE (0.6627, 0.5278) X_108 = Ψ(CIRCUMCENTER, INCENTER) (0.5320, 0.6114) X_92 = CEVAPOINT OF INCENTER AND CLAWSON POINT (0.5949, 0.3639) X_406 = EULER LINE INTERCEPT OF LINE X(10)X(33) (0.5745, 0.2970) X_281 = -CROSS CONJUGATE OF X(9) (0.5796, 0.3202) X_451 = -HIRST INVERSE OF X(424) (0.5621, 0.2645) X_318 = ISOTOMIC CONJUGATE OF X(77) (0.5514, 0.2839) X_475 = EULER LINE INTERCEPT OF LINE X(10)X(34) (-3.6531, -10.7644) X_155 = EIGENCENTER OF ORTHIC TRIANGLE (1.1658, 0.5033) X_651 = TRILINEAR POLE OF LINE X(1)X(3) (0.3048, 0.5599) X_1068 = -CROSS CONJUGATE OF X(4) (0.6478, 0.5373) A B C X46 X4 X1 X24 X108 X92 X406 X281 X451 X318 X475 X155 X651 X1068 (a, b, c) = (5, 6, 7) | AB = 1

X1068 (X46-CROSS CONJUGATE OF X4) 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 \(f(A,B,C) = 1 - \sec A (\cos B + \cos C)\)
Barycentrics: \(g(A,B,C) : g(B,C,A) : g(C,A,B)\), where \(g(A,B,C) = (\sin A) f(A,B,C)\)
Search Value (6, 9, 13): \(0.462985522392\)
▸ Incident Central Lines13 lines

{1, 4}, {8, 860}, {24, 108}, {92, 406}, {155, 651}, {158, 3542}, {281, 451}, {318, 475}, {377, 1060}, {429, 495}, {1038, 1074}, {1040, 1076}, {3157, 3193}

▸ Functional Relations4 relations