X1059

ISOGONAL CONJUGATE OF X1058

X1059 is the isogonal conjugate of X1058.
< 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) { 78, 999 }: Central Line L(78, 999) { 29, 1056 }: Central Line L(29, 1056) { 73, 1057 }: Central Line L(73, 1057) { 388, 1067 }: Central Line L(388, 1067) { 1036, 1066 }: Central Line L(1036, 1066) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1058 = POINT ALKALUROPS (0.5662, 0.2123) X_78 = ISOGONAL CONJUGATE OF X(34) (0.3835, 0.0491) X_999 = MIDPOINT OF X(1) AND X(57) (0.5926, 0.2722) X_29 = CEVAPOINT OF INCENTER AND ORTHOCENTER (0.5903, 0.3384) X_1056 = POINT ALCYONE (0.5756, 0.2499) X_73 = CROSSPOINT OF INCENTER AND CIRCUMCENTER (0.5487, 0.1428) X_1057 = ISOGONAL CONJUGATE OF X(1056) (0.5671, 0.2170) X_388 = ∩X(7)X(8) (0.5790, 0.2635) X_1067 = ISOGONAL CONJUGATE OF X(1066) (0.5526, 0.1758) X_1036 = ISOGONAL CONJUGATE OF X(388) (0.5632, 0.2044) X_1066 = HASTINGS POINT (0.5873, 0.2963) X_1059 = ISOGONAL CONJUGATE OF X(1058) (0.5764, 0.2549) A B C X1058 X78 X999 X29 X1056 X73 X1057 X388 X1067 X1036 X1066 X1059 (a, b, c) = (5, 6, 7) | AB = 1

X1059 (ISOGONAL CONJUGATE OF X1058) 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 \(f(A,B,C) = 1/(2 - \cos B \cos C)\)
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): \(1.209869729995\)
▸ Incident Central Lines5 lines

{29, 1056}, {73, 1057}, {78, 999}, {388, 1067}, {1036, 1066}

▸ Functional Relations1 relation