X1447

X350-BETH CONJUGATE OF X350

X1447 = crossdifference of every pair of points on line X663X1334
< 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, 7 }: Centroid–Gergonne Line { 56, 85 }: Central Line L(56, 85) { 75, 183 }: Central Line L(75, 183) { 25, 273 }: Central Line L(25, 273) { 87, 269 }: Central Line L(87, 269) { 241, 292 }: Central Line L(241, 292) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_350 = -HIRST INVERSE OF X(75) (-3.5227, -3.1370) X_2 = CENTROID (0.5374, 0.2000) X_7 = GERGONNE POINT (0.5903, 0.2769) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_85 = ISOTOMIC CONJUGATE OF X(9) (0.5610, 0.2421) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_183 = TRILINEAR PRODUCT X(75)X(182) (0.4700, 0.1275) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_273 = ISOGONAL CONJUGATE OF X(212) (0.6191, 0.4329) X_87 = -CROSS CONJUGATE OF X(1) (0.4794, 0.1691) X_269 = ISOGONAL CONJUGATE OF X(200) (0.6369, 0.3847) X_241 = -LINE CONJUGATE OF X(55) (1.1217, 1.2442) X_292 = -HIRST INVERSE OF X(291) (1.0127, 0.0417) X_1447 = -BETH CONJUGATE OF X(350) (1.1014, 1.0207) A B C X350 X2 X7 X56 X85 X75 X183 X25 X273 X87 X269 X241 X292 X1447 (a, b, c) = (5, 6, 7) | AB = 1

X1447 (X350-BETH CONJUGATE OF X350) 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 \(u : v : w\) = X350
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-0.757213340335\)
▸ Incident Central Lines19 lines

{2, 7}, {25, 273}, {36, 1111}, {56, 85}, {75, 183}, {77, 614}, {86, 1431}, {87, 269}, {105, 927}, {230, 1086}, {239, 385}, {241, 292}, {261, 552}, {320, 325}, {350, 1281}, {459, 1119}, {664, 1319}, {673, 910}, {1402, 1441}

▸ Functional Relations6 relations