X1039

ISOGONAL CONJUGATE OF X1038

X1039 is the isogonal conjugate of X1038.
< 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) { 7, 34 }: Central Line L(7, 34) { 8, 33 }: Central Line L(8, 33) { 29, 314 }: Central Line L(29, 314) { 9, 607 }: Central Line L(9, 607) { 943, 968 }: Central Line L(943, 968) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1038 = INTERSECTION OF LINES X(1)X(3) AND X(2)X(34) (0.5104, 0.1211) X_1 = INCENTER (0.5714, 0.2333) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_7 = GERGONNE POINT (0.5903, 0.2769) X_34 = -BETH CONJUGATE OF X(4) (0.6332, 0.4792) X_8 = NAGEL POINT (0.4694, 0.1333) X_33 = PERSPECTOR OF THE ORTHIC AND INTANGENTS TRIANGLES (0.6019, 0.3546) X_29 = CEVAPOINT OF INCENTER AND ORTHOCENTER (0.5903, 0.3384) X_314 = ISOTOMIC CONJUGATE OF X(65) (0.4457, 0.1206) X_9 = MITTENPUNKT (0.5110, 0.1615) X_607 = ISOGONAL CONJUGATE OF X(348) (0.6187, 0.3865) X_943 = ISOGONAL CONJUGATE OF X(942) (0.5528, 0.2043) X_968 = POINT ALDERAMIN (0.5557, 0.2126) X_1039 = ISOGONAL CONJUGATE OF X(1038) (0.6094, 0.3672) A B C X1038 X1 X25 X7 X34 X8 X33 X29 X314 X9 X607 X943 X968 X1039 (a, b, c) = (5, 6, 7) | AB = 1

X1039 (ISOGONAL CONJUGATE OF X1038) 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 \(f(A,B,C) = 1/(\cos A + \cos A \cos B \cos C)\)
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): \(5.506764807058\)
▸ Incident Central Lines9 lines

{1, 25}, {4, 1096}, {7, 34}, {8, 33}, {9, 607}, {21, 1040}, {29, 314}, {65, 1041}, {943, 968}

▸ Functional Relations1 relation