X1709

MIMOSA TRANSFORM OF X9

X1709 = reflection of X1 in X1012
< 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, 1012 }: Central Line L(1, 1012) { 4, 46 }: Central Line L(4, 46) { 11, 57 }: Central Line L(11, 57) { 30, 40 }: Central Line L(30, 40) { 1, 84 }: Central Line L(1, 84) 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_1012 = INTERCEPT OF EULER LINE AND LINE X(1)X(84) (0.5770, 0.3036) X_4 = ORTHOCENTER (0.6122, 0.3958) X_46 = -CEVA CONJUGATE OF X(1) (0.6917, 0.4543) X_11 = FEUERBACH POINT (0.7347, 0.0667) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_40 = BEVAN POINT (0.4286, -0.0292) X_84 = ISOGONAL CONJUGATE OF X(40) (0.6071, 0.6816) X_1709 = MIMOSA TRANSFORM OF X(9) (0.5826, 0.3739) A B C X1 X1012 X4 X46 X11 X57 X30 X40 X84 X1709 (a, b, c) = (5, 6, 7) | AB = 1

X1709 (MIMOSA TRANSFORM OF X9) 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 \(f(a,b,c) = - (\cos A)/x + (\cos B)/y + (\cos C)/z\),\(x : y : z\) = X9
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-8.418403088109\)
▸ Incident Central Lines17 lines

{1, 84}, {4, 46}, {9, 165}, {11, 57}, {30, 40}, {31, 990}, {33, 109}, {35, 1490}, {55, 971}, {63, 516}, {553, 946}, {774, 1448}, {846, 1742}, {968, 991}, {1707, 1711}, {1719, 1744}, {1730, 1889}

▸ Functional Relations5 relations