X277

ISOGONAL CONJUGATE OF X218

X277 is the isogonal conjugate of X218.
< 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, 105 }: Central Line L(3, 105) { 1, 142 }: Central Line L(1, 142) { 7, 218 }: Central Line L(7, 218) { 57, 169 }: Central Line L(57, 169) { 241, 278 }: Central Line L(241, 278) { 220, 1086 }: Central Line L(220, 1086) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_218 = -CEVA CONJUGATE OF X(55) (0.6557, 0.3333) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_105 = Λ(INCENTER, SYMMEDIAN POINT) (0.9714, -0.0933) X_1 = INCENTER (0.5714, 0.2333) X_142 = COMPLEMENT OF X(9) (0.5506, 0.2192) X_7 = GERGONNE POINT (0.5903, 0.2769) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_169 = -CEVA CONJUGATE OF X(1) (0.5497, 0.2510) X_241 = -LINE CONJUGATE OF X(55) (1.1217, 1.2442) X_278 = ISOGONAL CONJUGATE OF X(219) (0.6278, 0.4577) X_220 = -CEVA CONJUGATE OF X(55) (0.4826, 0.1278) X_1086 = CENTER OF HYPERBOLA {{A,B,C,X(2),X(7)|} (0.7687, 0.1000) X_277 = ISOGONAL CONJUGATE OF X(218) (0.4242, 0.1335) A B C X218 X3 X105 X1 X142 X7 X57 X169 X241 X278 X220 X1086 X277 (a, b, c) = (5, 6, 7) | AB = 1

X277 (ISOGONAL CONJUGATE OF X218) 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 \(f(A,B,C) = [\sec^{2}(A/2)]/[- \cos^{4} A/2 + \cos^{4} B/2 + \cos^{4} C/2]\)
Barycentrics: \(1/(a^{2} + b^{2} + c^{2} - 2 a b - 2 a c) : :\)
Search Value (6, 9, 13): \(19.939380009706\)
▸ Incident Central Lines7 lines

{1, 142}, {3, 105}, {7, 218}, {57, 169}, {220, 1086}, {241, 278}, {942, 1002}

▸ Functional Relations4 relations