X1443

X320-BETH CONJUGATE OF X320

X1443 = crossdifference of every pair of points on line X657X1334
< A B C >: Reference Triangle △ABC < K_a K_b K_c >: Anticomplementary Triangle △K_a K_b K_c [ A B ]: Sideline AB (Base c = 1) [ B C ]: Sideline BC (Side a) [ C A ]: Sideline CA (Side b) { 2, 1489 }: Central Line L(2, 1489) { 1, 7 }: Soddy Line { 57, 89 }: Central Line L(57, 89) { 44, 241 }: Central Line L(44, 241) { 60, 757 }: Central Line L(60, 757) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) K_a = Anticomplementary Vertex K_a (1.6122, 0.5999) K_b = Anticomplementary Vertex K_b (-0.3878, 0.5999) K_c = Anticomplementary Vertex K_c (0.3878, -0.5999) X_2 = CENTROID (0.5374, 0.2000) X_1489 = 3rd STEVANOVIC POINT (0.5675, 0.2288) X_1 = INCENTER (0.5714, 0.2333) X_7 = GERGONNE POINT (0.5903, 0.2769) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_89 = ISOGONAL CONJUGATE OF X(45) (0.5963, 0.2697) X_44 = -LINE CONJUGATE OF X(1) (2.1429, 2.0996) X_241 = -LINE CONJUGATE OF X(55) (1.1217, 1.2442) X_60 = ISOGONAL CONJUGATE OF X(12) (0.5790, 0.2258) X_757 = ISOGONAL CONJUGATE OF X(756) (0.5971, 0.2688) X_1443 = -BETH CONJUGATE OF X(320) (0.9441, 1.0954) A B C Ka Kb Kc X2 X1489 X1 X7 X57 X89 X44 X241 X60 X757 X1443 (a, b, c) = (5, 6, 7) | AB = 1

X1443 (X320-BETH CONJUGATE OF X320) 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 \(u : v : w\) = X320
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-0.469434119155\)
▸ Alternate Coordinates1 form

  • Trilinears: \(g(A,B,C) : g(B,C,A) : g(C,A,B)\), where \(g(A, B, C) = (1 - 2 \cos A)/(1 + \cos A)\)

▸ Incident Central Lines11 lines

{1, 7}, {44, 241}, {54, 1439}, {57, 89}, {59, 1155}, {60, 757}, {88, 1465}, {320, 1464}, {679, 1318}, {934, 953}, {1419, 1445}

▸ Functional Relations3 relations