X2829

ISOGONAL CONJUGATE OF X2745

X2829 is the isogonal conjugate of X2745.
< 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, 11 }: Central Line L(4, 11) { 20, 100 }: Central Line L(20, 100) { 3, 119 }: Central Line L(3, 119) { 46, 80 }: Central Line L(46, 80) { 30, 511 }: Central Line L(30, 511) { 40, 1145 }: Central Line L(40, 1145) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2745 = SR(X(104), X(108)) (0.0897, -0.2013) X_4 = ORTHOCENTER (0.6122, 0.3958) X_11 = FEUERBACH POINT (0.7347, 0.0667) X_20 = DE LONGCHAMPS POINT (0.3878, -0.1916) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.1429, 0.4666) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_119 = FEUERBACH ANTIPODE (0.3776, 0.4312) X_46 = -CEVA CONJUGATE OF X(1) (0.6917, 0.4543) X_80 = REFLECTION OF INCENTER IN FEUERBACH POINT (0.8980, -0.1000) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_40 = BEVAN POINT (0.4286, -0.0292) X_1145 = 3rd EHRMANN POINT (0.3061, 0.2999) X_2829 = ISOGONAL CONJUGATE OF X(2745) (0.3328, 0.7500) A B C X2745 X4 X11 X20 X100 X3 X119 X46 X80 X30 X511 X40 X1145 X2829 (a, b, c) = (5, 6, 7) | AB = 1

X2829 (ISOGONAL CONJUGATE OF X2745) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(1/f(a,b,c) : 1/f(b,c,a) : 1/f(c,a,b)\), where f(a,b,c) is as at X2745
Barycentrics: \(a/f(a,b,c) : b/f(b,c,a) : c/f(c,a,b)\)
▸ Incident Central Lines18 lines

{1, 1537}, {3, 119}, {4, 11}, {20, 100}, {30, 511}, {36, 1532}, {40, 1145}, {46, 80}, {355, 1158}, {944, 1317}, {946, 1387}, {962, 1320}, {990, 998}, {1012, 1478}, {1155, 1512}, {1319, 1519}, {1455, 1785}, {1862, 1885}

▸ Functional Relations1 relation