X1429

X239-BETH CONJUGATE OF X239

X1429 = crossdifference of every pair of points on line X210X650
< 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) { 1, 3 }: OI Line (Incenter–Circumcenter Line) { 83, 226 }: Central Line L(83, 226) { 7, 604 }: Central Line L(7, 604) { 239, 385 }: Central Line L(239, 385) { 552, 553 }: Central Line L(552, 553) { 73, 1244 }: Central Line L(73, 1244) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_239 = -LINE CONJUGATE OF X(42) (4.2109, 3.7992) X_1 = INCENTER (0.5714, 0.2333) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_83 = CEVAPOINT OF CENTROID AND SYMMEDIAN POINT (0.5651, 0.2360) X_226 = -CEVA CONJUGATE OF X(65) (0.5778, 0.2588) X_7 = GERGONNE POINT (0.5903, 0.2769) X_604 = -CEVA CONJUGATE OF X(31) (0.6442, 0.3744) X_385 = -HIRST INVERSE OF X(6) (2.2863, 2.0795) X_552 = POINT MAIA I (0.6112, 0.3127) X_553 = POINT MAIA II (0.5963, 0.2857) X_73 = CROSSPOINT OF INCENTER AND CIRCUMCENTER (0.5487, 0.1428) X_1244 = ISOGONAL CONJUGATE OF X(1009) (0.5903, 0.2249) X_1429 = -BETH CONJUGATE OF X(239) (0.9040, 0.8443) A B C X239 X1 X3 X83 X226 X7 X604 X385 X552 X553 X73 X1244 X1429 (a, b, c) = (5, 6, 7) | AB = 1

X1429 (X239-BETH CONJUGATE OF X239) 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 \(u : v : w\) = X239
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-0.332860391367\)
▸ Incident Central Lines12 lines

{1, 3}, {6, 1423}, {7, 604}, {73, 1244}, {81, 1432}, {83, 226}, {222, 1424}, {238, 1284}, {239, 385}, {552, 553}, {651, 1404}, {1458, 1462}

▸ Functional Relations5 relations