X951

ISOGONAL CONJUGATE OF X950

X951 is the isogonal conjugate of X950.
< 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) { 57, 78 }: Central Line L(57, 78) { 29, 226 }: Central Line L(29, 226) { 56, 219 }: Central Line L(56, 219) { 73, 284 }: Central Line L(73, 284) { 77, 738 }: Central Line L(77, 738) { 946, 1067 }: Central Line L(946, 1067) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_73 = CROSSPOINT OF INCENTER AND CIRCUMCENTER (0.5487, 0.1428) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_78 = ISOGONAL CONJUGATE OF X(34) (0.3835, 0.0491) X_29 = CEVAPOINT OF INCENTER AND ORTHOCENTER (0.5903, 0.3384) X_226 = -CEVA CONJUGATE OF X(65) (0.5778, 0.2588) X_219 = -CEVA CONJUGATE OF X(55) (0.4277, 0.0625) X_284 = -CROSS CONJUGATE OF X(21) (0.5646, 0.2088) X_77 = ISOGONAL CONJUGATE OF X(33) (0.5270, 0.1305) X_738 = ISOGONAL CONJUGATE OF X(728) (0.6449, 0.4466) X_946 = MIDPOINT OF X(1) AND X(4) (0.5918, 0.3145) X_1067 = ISOGONAL CONJUGATE OF X(1066) (0.5526, 0.1758) X_951 = ISOGONAL CONJUGATE OF X(950) (0.5800, 0.2727) A B C X56 X73 X57 X78 X29 X226 X219 X284 X77 X738 X946 X1067 X951 (a, b, c) = (5, 6, 7) | AB = 1

X951 (ISOGONAL CONJUGATE OF X950) 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 \(f(a,b,c) = a/[(b + c - a)[2a^{3} + (b + c)(a^{2} + (b - c)^{2})]]\)
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): \(0.728817415227\)
▸ Incident Central Lines7 lines

{29, 226}, {56, 219}, {57, 78}, {73, 284}, {77, 738}, {946, 1067}, {947, 1066}

▸ Functional Relations2 relations