X1066

HASTINGS POINT

X1066 = isogonal conjugate of X1067
< 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 { 222, 601 }: Central Line L(222, 601) { 42, 942 }: Central Line L(42, 942) { 3, 1037 }: Central Line L(3, 1037) { 517, 1042 }: Central Line L(517, 1042) { 774, 912 }: Central Line L(774, 912) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1067 = ISOGONAL CONJUGATE OF X(1066) (0.5526, 0.1758) X_1 = INCENTER (0.5714, 0.2333) X_4 = ORTHOCENTER (0.6122, 0.3958) X_222 = -CEVA CONJUGATE OF X(56) (0.5653, 0.1568) X_601 = INTERSECTION OF LINES X(3)X(31) AND X(55)X(255) (0.5761, 0.2252) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_942 = INCIRCLE-INVERSE OF X(36) (0.5878, 0.2633) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_1037 = CEVAPOINT OF X(55) AND X(56) (0.5823, 0.2853) X_517 = ISOGONAL CONJUGATE OF X(104) (0.8180, 0.7154) X_1042 = CROSSPOINT OF X(1) AND X(64) (0.6427, 0.3981) X_774 = CROSSPOINT OF X(1) AND X(158) (0.6363, 0.3186) X_912 = -CEVA CONJUGATE OF X(3) (0.0031, -0.0428) X_1066 = HASTINGS POINT (0.5873, 0.2963) A B C X1067 X1 X4 X222 X601 X42 X942 X3 X1037 X517 X1042 X774 X912 X1066 (a, b, c) = (5, 6, 7) | AB = 1

X1066 (HASTINGS POINT) 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 \(f(A,B,C) = 1 - \cos A (\cos B + \cos C)\)
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): \(0.996518058550\)
▸ Incident Central Lines9 lines

{1, 4}, {3, 1037}, {42, 942}, {222, 601}, {517, 1042}, {774, 912}, {947, 951}, {976, 1060}, {1036, 1059}

▸ Functional Relations2 relations