X1734

MIMOSA TRANSFORM OF X101

X1734 = reflection of X1 in X905
< 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, 905 }: Central Line L(1, 905) { 240, 522 }: Central Line L(240, 522) { 484, 513 }: Central Line L(484, 513) { 100, 1110 }: Central Line L(100, 1110) { 649, 830 }: Central Line L(649, 830) 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_905 = POINT ACHERNAR (5.6190, -0.6999) X_240 = -LINE CONJUGATE OF X(48) (0.7457, 0.8594) X_522 = ISOGONAL CONJUGATE OF X(109) (-0.0318, 0.3430) X_484 = 1st EVANS PERSPECTOR (2.0952, 3.0327) X_513 = ISOGONAL CONJUGATE OF X(100) (1.0529, -0.0806) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.1429, 0.4666) X_1110 = TRILINEAR SQUARE OF X(101) (0.5057, 0.3942) X_649 = CROSSDIFFERENCE OF X(1) and X(2) (-21.0000, 14.6969) X_830 = ODD (1, 3) INFINITY POINT (1.0590, -0.0690) X_1734 = MIMOSA TRANSFORM OF X(101) (10.6667, -1.6330) A B C X1 X905 X240 X522 X484 X513 X100 X1110 X649 X830 X1734 (a, b, c) = (5, 6, 7) | AB = 1

X1734 (MIMOSA TRANSFORM OF X101) 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 \(f(a,b,c) = - (\cos A)/x + (\cos B)/y + (\cos C)/z\),\(x : y : z\) = X101
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-18.915357129638\)
▸ Alternate Coordinates1 form

  • Trilinears: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = (b - c)(b^{2} + c^{2} + bc - ab - ac)\) (M. Iliev, 5/13/07)

▸ Incident Central Lines6 lines

{1, 905}, {100, 1110}, {240, 522}, {484, 513}, {512, 1491}, {649, 830}

▸ Functional Relations5 relations