X3108

DC(X83)

For an introduction to the DC and CD mappings, see the discussion just before X2979.
< 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) { 39, 251 }: Central Line L(39, 251) { 25, 1180 }: Central Line L(25, 1180) { 111, 1194 }: Central Line L(111, 1194) { 305, 1239 }: Central Line L(305, 1239) { 6, 1627 }: Central Line L(6, 1627) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3005 = (DE LONGCHAMPS LINE)∩(LEMOINE AXIS) (12.7640, -5.7469) X_110 = FOCUS OF KIEPERT PARABOLA (0.2516, 0.5478) X_39 = BROCARD MIDPOINT (0.5778, 0.2305) X_251 = ISOGONAL CONJUGATE OF X(141) (0.6177, 0.3042) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_1180 = 2nd SARAGOSSA POINT OF X(2) (0.5852, 0.2361) X_111 = PARRY POINT (0.9885, -0.0457) X_1194 = 3rd SARAGOSSA POINT OF X(2) (0.5959, 0.2442) X_305 = ISOTOMIC CONJUGATE OF X(25) (0.3258, 0.0397) X_1239 = ISOTOMIC CONJUGATE OF X(1180) (0.4817, 0.1646) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_1627 = TCC-PERSPECTOR OF X(251) (0.6795, 0.3846) X_3108 = DC(X(83)) (0.5882, 0.2498) A B C X3005 X110 X39 X251 X25 X1180 X111 X1194 X305 X1239 X6 X1627 X3108 (a, b, c) = (5, 6, 7) | AB = 1

X3108 (DC(X83)) 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 \(f(a,b,c) = a/(2a^{2} + b^{2} + c^{2})\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(1.252808863131\)
▸ Incident Central Lines5 lines

{6, 1627}, {25, 1180}, {39, 251}, {111, 1194}, {305, 1239}

▸ Functional Relations6 relations