X977

ISOGONAL CONJUGATE OF X976

X977 is the isogonal conjugate of X976.
< 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) { 22, 56 }: Central Line L(22, 56) { 106, 833 }: Central Line L(106, 833) { 58, 982 }: Central Line L(58, 982) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_976 = INTERSECTION OF LINES X(1)X(2) AND X(3)X(38) (0.5520, 0.2143) X_22 = EXETER POINT (0.4143, -0.1221) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_106 = Λ(INCENTER, CENTROID) (1.0000, 0.0000) X_833 = o-(1, 4) CIRCUMCIRCLE POINT (0.1829, 0.5019) X_58 = ISOGONAL CONJUGATE OF X(10) (0.6107, 0.2850) X_982 = INTERSECTION OF LINES X(1)X(3) AND X(2)X(38) (0.5508, 0.1955) X_977 = ISOGONAL CONJUGATE OF X(976) (0.5890, 0.2525) A B C X976 X22 X56 X106 X833 X58 X982 X977 (a, b, c) = (5, 6, 7) | AB = 1

X977 (ISOGONAL CONJUGATE OF X976) 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 \(f(a,b,c) = 1/[a^{3} + (b + c)(b^{2} + c^{2})]\)
Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = af(a,b,c)\)
Search Value (6, 9, 13): \(1.317316683877\)
▸ Incident Central Lines3 lines

{22, 56}, {58, 982}, {106, 833}

▸ Functional Relations1 relation