X1069

X255-CROSS CONJUGATE OF X3

X1069 = isogonal conjugate of X1068
< 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) { 11, 68 }: Central Line L(11, 68) { 1, 90 }: Central Line L(1, 90) { 496, 613 }: Central Line L(496, 613) { 394, 1062 }: Central Line L(394, 1062) { 916, 1037 }: Central Line L(916, 1037) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_255 = ISOGONAL CONJUGATE OF X(158) (0.4217, 0.0365) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_11 = FEUERBACH POINT (0.7347, 0.0667) X_68 = PRASOLOV POINT (-0.0535, -0.0055) X_1 = INCENTER (0.5714, 0.2333) X_90 = -CROSS CONJUGATE OF X(1) (0.1022, 0.0201) X_496 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(495) (0.5843, 0.2201) X_613 = INTERSECTION OF LINES X(1)X(6) AND X(56)X(511) (0.7698, 0.2310) X_394 = -CEVA CONJUGATE OF X(3) (0.3778, 0.0284) X_1062 = INTERSECTION OF LINES X(1)X(3) AND X(5)X(33) (0.4633, 0.0347) X_916 = -CEVA CONJUGATE OF X(3) (0.0224, -0.0814) X_1037 = CEVAPOINT OF X(55) AND X(56) (0.5823, 0.2853) X_1069 = -CROSS CONJUGATE OF X(3) (0.0709, 0.0059) A B C X255 X3 X11 X68 X1 X90 X496 X613 X394 X1062 X916 X1037 X1069 (a, b, c) = (5, 6, 7) | AB = 1

X1069 (X255-CROSS CONJUGATE OF X3) 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 \(f(A,B,C) = 1/[1 - \sec A (\cos B + \cos C)]\)
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): \(2.267320739643\)
▸ Incident Central Lines5 lines

{1, 90}, {11, 68}, {394, 1062}, {496, 613}, {916, 1037}

▸ Functional Relations4 relations