X1067

ISOGONAL CONJUGATE OF X1066

X1067 is the isogonal conjugate of X1066.
< 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) { 3, 496 }: Central Line L(3, 496) { 4, 1037 }: Central Line L(4, 1037) { 388, 1059 }: Central Line L(388, 1059) { 946, 951 }: Central Line L(946, 951) { 947, 950 }: Central Line L(947, 950) { 1036, 1058 }: Central Line L(1036, 1058) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1066 = HASTINGS POINT (0.5873, 0.2963) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_496 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(495) (0.5843, 0.2201) X_4 = ORTHOCENTER (0.6122, 0.3958) X_1037 = CEVAPOINT OF X(55) AND X(56) (0.5823, 0.2853) X_388 = ∩X(7)X(8) (0.5790, 0.2635) X_1059 = ISOGONAL CONJUGATE OF X(1058) (0.5764, 0.2549) X_946 = MIDPOINT OF X(1) AND X(4) (0.5918, 0.3145) X_951 = ISOGONAL CONJUGATE OF X(950) (0.5800, 0.2727) X_947 = ISOGONAL CONJUGATE OF X(946) (0.5457, 0.1609) X_950 = CROSSPOINT OF X(8) AND X(29) (0.5621, 0.1961) X_1036 = ISOGONAL CONJUGATE OF X(388) (0.5632, 0.2044) X_1058 = POINT ALKALUROPS (0.5662, 0.2123) X_1067 = ISOGONAL CONJUGATE OF X(1066) (0.5526, 0.1758) A B C X1066 X3 X496 X4 X1037 X388 X1059 X946 X951 X947 X950 X1036 X1058 X1067 (a, b, c) = (5, 6, 7) | AB = 1

X1067 (ISOGONAL CONJUGATE OF X1066) 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 \(f(A,B,C) = 1/[1 - \cos A (\cos B + \cos C)]\)
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): \(2.266930092148\)
▸ Incident Central Lines6 lines

{3, 496}, {4, 1037}, {388, 1059}, {946, 951}, {947, 950}, {1036, 1058}

▸ Functional Relations1 relation