X1754

MIMOSA TRANSFORM OF X284

< 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, 3 }: OI Line (Incenter–Circumcenter Line) { 20, 58 }: Central Line L(20, 58) { 109, 278 }: Central Line L(109, 278) { 212, 226 }: Central Line L(212, 226) { 31, 516 }: Central Line L(31, 516) { 4, 580 }: Central Line L(4, 580) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1 = INCENTER (0.5714, 0.2333) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_20 = DE LONGCHAMPS POINT (0.3878, -0.1916) X_58 = ISOGONAL CONJUGATE OF X(10) (0.6107, 0.2850) X_109 = Ψ(INCENTER, CIRCUMCENTER) (0.3636, 0.5938) X_278 = ISOGONAL CONJUGATE OF X(219) (0.6278, 0.4577) X_212 = -CEVA CONJUGATE OF X(41) (0.4719, 0.0786) X_226 = -CEVA CONJUGATE OF X(65) (0.5778, 0.2588) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_516 = ISOGONAL CONJUGATE OF X(103) (0.7703, 0.7386) X_4 = ORTHOCENTER (0.6122, 0.3958) X_580 = ORTHOGONAL OF X(284) (0.7089, 0.4470) X_1754 = MIMOSA TRANSFORM OF X(284) (0.6792, 0.4313) A B C X1 X3 X20 X58 X109 X278 X212 X226 X31 X516 X4 X580 X1754 (a, b, c) = (5, 6, 7) | AB = 1

X1754 (MIMOSA TRANSFORM OF X284) 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 \(f(a,b,c) = - (\cos A)/x + (\cos B)/y + (\cos C)/z\),\(x : y : z\) = X284
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-3.379056899666\)
▸ Incident Central Lines29 lines

{1, 3}, {4, 580}, {5, 582}, {20, 58}, {25, 1730}, {31, 516}, {33, 1708}, {47, 1770}, {63, 990}, {81, 991}, {109, 278}, {184, 851}, {209, 916}, {212, 226}, {219, 1376}, {238, 1699}, {255, 1074}, {283, 377}, {386, 411}, {394, 1004}, {498, 1794}, {579, 1172}, {595, 962}, {602, 946}, {846, 1744}, {950, 1451}, {1707, 1709}, {1726, 1824}, {1743, 1750}

▸ Functional Relations2 relations