X1442

X319-BETH CONJUGATE OF X319

< 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, 7 }: Soddy Line { 8, 326 }: Central Line L(8, 326) { 37, 651 }: Central Line L(37, 651) { 86, 664 }: Central Line L(86, 664) { 2, 914 }: Central Line L(2, 914) { 74, 934 }: Central Line L(74, 934) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_319 = ISOTOMIC CONJUGATE OF X(79) (0.4549, 0.1161) X_1 = INCENTER (0.5714, 0.2333) X_7 = GERGONNE POINT (0.5903, 0.2769) X_8 = NAGEL POINT (0.4694, 0.1333) X_326 = ISOTOMIC CONJUGATE OF X(158) (0.3354, 0.0219) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_651 = TRILINEAR POLE OF LINE X(1)X(3) (0.3048, 0.5599) X_86 = CEVAPOINT OF INCENTER AND CENTROID (0.5534, 0.2171) X_664 = TRILINEAR POLE OF LINE X(2)X(7) (0.2391, 0.5142) X_2 = CENTROID (0.5374, 0.2000) X_914 = ISOGONAL CONJUGATE OF X(913) (-2.5447, -1.0613) X_74 = ISOGONAL CONJUGATE OF EULER INFINITY POINT (0.7484, -0.3437) X_934 = -CROSS CONJUGATE OF X(57) (0.4269, 0.6071) X_1442 = -BETH CONJUGATE OF X(319) (0.5612, 0.2097) A B C X319 X1 X7 X8 X326 X37 X651 X86 X664 X2 X914 X74 X934 X1442 (a, b, c) = (5, 6, 7) | AB = 1

X1442 (X319-BETH CONJUGATE OF X319) 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 \(u : v : w\) = X319
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(3.070035914723\)
▸ 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 Lines13 lines

{1, 7}, {2, 914}, {8, 326}, {37, 651}, {65, 1014}, {74, 934}, {81, 1214}, {86, 664}, {226, 1029}, {241, 1100}, {319, 1273}, {1082, 1250}, {1445, 1449}