X1445

X344-BETH CONJUGATE OF X344

X1445 = {X9,X57}-harmonic conjugate of X7
< 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 { 6, 77 }: Central Line L(6, 77) { 56, 78 }: Central Line L(56, 78) { 19, 273 }: Central Line L(19, 273) { 40, 390 }: Central Line L(40, 390) { 46, 516 }: Central Line L(46, 516) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_344 = ISOTOMIC CONJUGATE OF X(277) (0.6218, 0.2693) X_2 = CENTROID (0.5374, 0.2000) X_7 = GERGONNE POINT (0.5903, 0.2769) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_77 = ISOGONAL CONJUGATE OF X(33) (0.5270, 0.1305) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_78 = ISOGONAL CONJUGATE OF X(34) (0.3835, 0.0491) X_19 = CLAWSON POINT (0.6246, 0.4244) X_273 = ISOGONAL CONJUGATE OF X(212) (0.6191, 0.4329) X_40 = BEVAN POINT (0.4286, -0.0292) X_390 = REFLECTION OF GERGONNE POINT IN INCENTER (0.5526, 0.1897) X_46 = -CEVA CONJUGATE OF X(1) (0.6917, 0.4543) X_516 = ISOGONAL CONJUGATE OF X(103) (0.7703, 0.7386) X_1445 = -BETH CONJUGATE OF X(344) (0.6570, 0.3740) A B C X344 X2 X7 X6 X77 X56 X78 X19 X273 X40 X390 X46 X516 X1445 (a, b, c) = (5, 6, 7) | AB = 1

X1445 (X344-BETH CONJUGATE OF X344) 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 \(u : v : w\) = X344
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-0.090617388587\)
▸ Incident Central Lines15 lines

{1, 1170}, {2, 7}, {6, 77}, {19, 273}, {40, 390}, {44, 1418}, {46, 516}, {56, 78}, {65, 1001}, {169, 1446}, {269, 651}, {942, 954}, {1038, 1451}, {1419, 1443}, {1442, 1449}

▸ Functional Relations2 relations