X3895

X495com[INVERSE(n(4th EULER TRIANGLE))]

< 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) { 8, 9 }: Central Line L(8, 9) { 1, 88 }: Central Line L(1, 88) { 40, 145 }: Central Line L(40, 145) { 63, 519 }: Central Line L(63, 519) { 78, 3057 }: Central Line L(78, 3057) { 46, 3244 }: Central Line L(46, 3244) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_8 = NAGEL POINT (0.4694, 0.1333) X_9 = MITTENPUNKT (0.5110, 0.1615) X_1 = INCENTER (0.5714, 0.2333) X_88 = ISOGONAL CONJUGATE OF X(44) (1.0000, 0.0000) X_40 = BEVAN POINT (0.4286, -0.0292) X_145 = ANTICOMPLEMENT OF NAGEL POINT (0.6735, 0.3333) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4566, 0.0823) X_519 = ISOGONAL CONJUGATE OF X(106) (0.9566, 0.6107) X_78 = ISOGONAL CONJUGATE OF X(34) (0.3835, 0.0491) X_3057 = INTERSECTION OF LINES X(1)X(3) AND X(10)X(11) (0.5388, 0.1733) X_46 = -CEVA CONJUGATE OF X(1) (0.6917, 0.4543) X_3244 = REFLECTION OF X(10) IN X(1) (0.6224, 0.2833) X_3895 = com[INVERSE(n(4th EULER TRIANGLE))] (0.5966, 0.2196) A B C X8 X9 X1 X88 X40 X145 X63 X519 X78 X3057 X46 X3244 X3895 (a, b, c) = (5, 6, 7) | AB = 1

X3895 (X495com[INVERSE(n(4th 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 \(f(a,b,c) = a(b + c - a)(a^{2} + b^{2} + c^{2} + 2ab + 2ac - 4bc)\)
Search Value (6, 9, 13): \(1.286360072162\)
▸ Incident Central Lines14 lines

{1, 88}, {8, 9}, {40, 145}, {46, 3244}, {57, 3241}, {63, 519}, {78, 3057}, {960, 3711}, {1706, 3616}, {1837, 3036}, {2320, 3601}, {3305, 3679}, {3333, 3623}, {3338, 3635}