X1425

X201-BETH CONJUGATE OF X201

X1425 = crosspoint of X65 and X73
< 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) { 34, 51 }: Central Line L(34, 51) { 12, 125 }: Central Line L(12, 125) { 1, 185 }: Central Line L(1, 185) { 56, 184 }: Central Line L(56, 184) { 25, 221 }: Central Line L(25, 221) { 65, 225 }: Central Line L(65, 225) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_201 = -CEVA CONJUGATE OF X(12) (0.4897, 0.1062) X_34 = -BETH CONJUGATE OF X(4) (0.6332, 0.4792) X_51 = CENTROID OF ORTHIC TRIANGLE (0.6093, 0.3186) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_125 = CENTER OF JERABEK HYPERBOLA (0.6803, 0.0260) X_1 = INCENTER (0.5714, 0.2333) X_185 = NAGEL POINT OF THE ORTHIC TRIANGLE (0.6033, 0.1643) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_184 = INVERSE OF X(125) IN THE BROCARD CIRCLE (0.5788, 0.1496) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_221 = -CEVA CONJUGATE OF X(56) (0.5474, -0.0688) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_225 = -CEVA CONJUGATE OF X(65) (0.6246, 0.4451) X_1425 = -BETH CONJUGATE OF X(201) (0.5904, 0.1922) A B C X201 X34 X51 X12 X125 X1 X185 X56 X184 X25 X221 X65 X225 X1425 (a, b, c) = (5, 6, 7) | AB = 1

X1425 (X201-BETH CONJUGATE OF X201) 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 \(f(a,b,c) = (1 - \cos A)u(a,b,c)\), where \(u : v : w\) = X201
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-0.259059806236\)
▸ Incident Central Lines16 lines

{1, 185}, {6, 1398}, {12, 125}, {25, 221}, {34, 51}, {55, 1204}, {56, 184}, {65, 225}, {72, 307}, {73, 228}, {181, 1254}, {213, 1042}, {217, 1015}, {999, 1181}, {1093, 1148}, {1106, 1401}

▸ Functional Relations3 relations