X1455

X515-BETH CONJUGATE OF X515

X1455 = X104-Ceva conjugate of X56
< 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) { 25, 34 }: Central Line L(25, 34) { 1, 84 }: Central Line L(1, 84) { 3, 227 }: Central Line L(3, 227) { 37, 478 }: Central Line L(37, 478) { 109, 517 }: Central Line L(109, 517) { 117, 515 }: Central Line L(117, 515) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_515 = ISOGONAL CONJUGATE OF X(102) (0.6804, 0.7691) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_34 = -BETH CONJUGATE OF X(4) (0.6332, 0.4792) X_1 = INCENTER (0.5714, 0.2333) X_84 = ISOGONAL CONJUGATE OF X(40) (0.6071, 0.6816) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_227 = -CEVA CONJUGATE OF X(65) (0.4792, -0.0460) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_478 = CENTER OF YIU CONIC (0.5030, -0.3520) X_109 = Ψ(INCENTER, CIRCUMCENTER) (0.3636, 0.5938) X_517 = ISOGONAL CONJUGATE OF X(104) (0.8180, 0.7154) X_117 = MIDPOINT OF X(4) AND X(109) (0.4879, 0.4948) X_1455 = -BETH CONJUGATE OF X(515) (0.6407, 1.1028) A B C X515 X25 X34 X1 X84 X3 X227 X37 X478 X109 X517 X117 X1455 (a, b, c) = (5, 6, 7) | AB = 1

X1455 (X515-BETH CONJUGATE OF X515) 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 \(u : v : w\) = X515
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-0.190848934705\)
▸ Incident Central Lines14 lines

{1, 84}, {3, 227}, {25, 34}, {36, 1465}, {37, 478}, {65, 603}, {73, 820}, {109, 517}, {117, 515}, {513, 663}, {608, 1108}, {910, 1415}, {958, 1038}, {993, 1214}

▸ Functional Relations2 relations