X3887

X2826com[INVERSE(n(3rd EULER TRIANGLE))]

X3887 = crossdifference of every pair of points on line X6X244
< 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) { 11, 116 }: Central Line L(11, 116) { 100, 101 }: Central Line L(100, 101) { 103, 104 }: Central Line L(103, 104) { 118, 119 }: Central Line L(118, 119) { 149, 150 }: Central Line L(149, 150) { 152, 153 }: Central Line L(152, 153) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1308 = COLLINGS TRANSFORM OF X(661) (1.0102, 0.0916) X_11 = FEUERBACH POINT (0.7347, 0.0667) X_116 = MIDPOINT OF X(4) AND X(103) (0.6990, 0.0375) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.1429, 0.4666) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.2143, 0.5249) X_103 = ANTIPODE OF X(101) (0.7857, -0.3208) X_104 = ANTIPODE OF X(100) (0.8571, -0.2624) X_118 = MIDPOINT OF X(4) AND X(101) (0.4133, 0.4603) X_119 = FEUERBACH ANTIPODE (0.3776, 0.4312) X_149 = REFLECTION OF X(20) IN X(104) (1.3265, -0.3333) X_150 = REFLECTION OF X(20) IN X(103) (1.1837, -0.4499) X_152 = REFLECTION OF X(20) IN X(101) (0.0408, 1.2414) X_153 = REFLECTION OF X(20) IN X(100) (-0.1020, 1.1248) X_3887 = com[INVERSE(n(3rd EULER TRIANGLE))] (0.9920, 0.5711) A B C X1308 X11 X116 X100 X101 X103 X104 X118 X119 X149 X150 X152 X153 X3887 (a, b, c) = (5, 6, 7) | AB = 1

X3887 (X2826com[INVERSE(n(3rd EULER TRIANGLE))]) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Barycentrics: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = a(b - c)(a^{2} + b^{2} + c^{2} - 2ab - 2ac + bc)\)
▸ Linear Combinations1 combination
▸ Incident Central Lines17 lines

{1, 2254}, {10, 3716}, {11, 116}, {30, 511}, {80, 885}, {100, 101}, {103, 104}, {118, 119}, {149, 150}, {152, 153}, {214, 3126}, {663, 1734}, {1022, 1280}, {1317, 1362}, {3032, 3033}, {3036, 3041}, {3045, 3046}

▸ Functional Relations5 relations