X959

ISOGONAL CONJUGATE OF X958

X959 is the isogonal conjugate of X958.
< 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) { 2, 65 }: Central Line L(2, 65) { 56, 81 }: Central Line L(56, 81) { 8, 181 }: Central Line L(8, 181) { 7, 274 }: Central Line L(7, 274) { 193, 330 }: Central Line L(193, 330) { 1, 573 }: Central Line L(1, 573) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_958 = INTERSECTION OF LINES X(1)X(6) AND X(2)X(12) (0.5166, 0.1682) X_2 = CENTROID (0.5374, 0.2000) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_81 = CEVAPOINT OF INCENTER AND SYMMEDIAN POINT (0.5849, 0.2510) X_8 = NAGEL POINT (0.4694, 0.1333) X_181 = APOLLONIUS POINT (0.6163, 0.3093) X_7 = GERGONNE POINT (0.5903, 0.2769) X_274 = ISOGONAL CONJUGATE OF X(213) (0.5168, 0.1843) X_193 = -CEVA CONJUGATE OF X(2) (0.7878, 0.4690) X_330 = ISOTOMIC CONJUGATE OF X(192) (0.4364, 0.1391) X_1 = INCENTER (0.5714, 0.2333) X_573 = ORTHOHARMONIC OF X(58) (0.4583, 0.2009) X_959 = ISOGONAL CONJUGATE OF X(958) (0.6111, 0.3031) A B C X958 X2 X65 X56 X81 X8 X181 X7 X274 X193 X330 X1 X573 X959 (a, b, c) = (5, 6, 7) | AB = 1

X959 (ISOGONAL CONJUGATE OF X958) 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 \(f(a,b,c) = 1/[(b + c - a)(a^{2} + ab + ac + 2bc)]\)
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): \(0.435147823461\)
▸ Incident Central Lines9 lines

{1, 573}, {2, 65}, {6, 961}, {7, 274}, {8, 181}, {28, 608}, {56, 81}, {57, 1042}, {193, 330}

▸ Functional Relations1 relation