X1041

ISOGONAL CONJUGATE OF X1040

The trilinear polar of X1041 passes through X650.
< 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) { 7, 33 }: Central Line L(7, 33) { 8, 34 }: Central Line L(8, 34) { 19, 294 }: Central Line L(19, 294) { 9, 608 }: Central Line L(9, 608) { 1, 1037 }: Central Line L(1, 1037) { 21, 1038 }: Central Line L(21, 1038) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_33 = PERSPECTOR OF THE ORTHIC AND INTANGENTS TRIANGLES (0.6019, 0.3546) X_34 = -BETH CONJUGATE OF X(4) (0.6332, 0.4792) X_7 = GERGONNE POINT (0.5903, 0.2769) X_8 = NAGEL POINT (0.4694, 0.1333) X_19 = CLAWSON POINT (0.6246, 0.4244) X_294 = ISOGONAL CONJUGATE OF X(241) (0.9276, -0.0575) X_9 = MITTENPUNKT (0.5110, 0.1615) X_608 = ISOGONAL CONJUGATE OF X(345) (0.6361, 0.4975) X_1 = INCENTER (0.5714, 0.2333) X_1037 = CEVAPOINT OF X(55) AND X(56) (0.5823, 0.2853) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_1038 = INTERSECTION OF LINES X(1)X(3) AND X(2)X(34) (0.5104, 0.1211) X_1041 = ISOGONAL CONJUGATE OF X(1040) (0.6147, 0.4401) A B C X33 X34 X7 X8 X19 X294 X9 X608 X1 X1037 X21 X1038 X1041 (a, b, c) = (5, 6, 7) | AB = 1

X1041 (ISOGONAL CONJUGATE OF X1040) 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): \(-0.433837286183\)
▸ Incident Central Lines7 lines

{1, 1037}, {7, 33}, {8, 34}, {9, 608}, {19, 294}, {21, 1038}, {65, 1039}

▸ Functional Relations2 relations