X1036

ISOGONAL CONJUGATE OF X388

X1036 is the isogonal conjugate of X388.
< 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, 25 }: Central Line L(1, 25) { 3, 31 }: Central Line L(3, 31) { 55, 78 }: Central Line L(55, 78) { 56, 77 }: Central Line L(56, 77) { 41, 219 }: Central Line L(41, 219) { 21, 332 }: Central Line L(21, 332) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_388 = ∩X(7)X(8) (0.5790, 0.2635) X_1 = INCENTER (0.5714, 0.2333) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_78 = ISOGONAL CONJUGATE OF X(34) (0.3835, 0.0491) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_77 = ISOGONAL CONJUGATE OF X(33) (0.5270, 0.1305) X_41 = -CEVA CONJUGATE OF X(31) (0.5823, 0.2244) X_219 = -CEVA CONJUGATE OF X(55) (0.4277, 0.0625) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_332 = ISOTOMIC CONJUGATE OF X(225) (0.3595, 0.0434) X_1036 = ISOGONAL CONJUGATE OF X(388) (0.5632, 0.2044) A B C X388 X1 X25 X3 X31 X55 X78 X56 X77 X41 X219 X21 X332 X1036 (a, b, c) = (5, 6, 7) | AB = 1

X1036 (ISOGONAL CONJUGATE OF X388) 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 \(f(A,B,C) = 1/(1 + \cos B \cos C)\)
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): \(2.300493366682\)
▸ Incident Central Lines13 lines

{1, 25}, {3, 31}, {4, 1065}, {21, 332}, {29, 497}, {41, 219}, {55, 78}, {56, 77}, {73, 1037}, {282, 380}, {581, 947}, {1058, 1067}, {1059, 1066}

▸ Functional Relations1 relation