X2064

ORION TRANSFORM OF X75

< 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) { 76, 85 }: Central Line L(76, 85) { 81, 314 }: Central Line L(81, 314) { 278, 345 }: Central Line L(278, 345) { 329, 1264 }: Central Line L(329, 1264) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_76 = 3rd BROCARD POINT (0.4567, 0.1388) X_85 = ISOTOMIC CONJUGATE OF X(9) (0.5610, 0.2421) X_81 = CEVAPOINT OF INCENTER AND SYMMEDIAN POINT (0.5849, 0.2510) X_314 = ISOTOMIC CONJUGATE OF X(65) (0.4457, 0.1206) X_278 = ISOGONAL CONJUGATE OF X(219) (0.6278, 0.4577) X_345 = ISOTOMIC CONJUGATE OF X(278) (0.3405, 0.0381) X_329 = ISOTOMIC CONJUGATE OF X(189) (0.3847, -0.0222) X_1264 = ISOTOMIC CONJUGATE OF X(1118) (0.2370, 0.0091) X_2064 = ORION TRANSFORM OF X(75) (0.3100, -0.0064) A B C X76 X85 X81 X314 X278 X345 X329 X1264 X2064 (a, b, c) = (5, 6, 7) | AB = 1

X2064 (ORION TRANSFORM OF X75) 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 \(f(a,b,c) = b^{2}c^{2}(a^{4} - b^{4} - c^{4} + a^{2}bc - b^{3}c - bc^{3})\) (M. Iliev, 5/13/07)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(6.634076722831\)
▸ Incident Central Lines4 lines

{76, 85}, {81, 314}, {278, 345}, {329, 1264}