X3889

X1656com[INVERSE(n(3rd 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) { 1, 21 }: Central Line L(1, 21) { 8, 354 }: Central Line L(8, 354) { 145, 942 }: Central Line L(145, 942) { 65, 3241 }: Central Line L(65, 3241) { 78, 3243 }: Central Line L(78, 3243) { 100, 3338 }: Central Line L(100, 3338) 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_21 = SCHIFFLER POINT (0.5287, 0.1771) X_8 = NAGEL POINT (0.4694, 0.1333) X_354 = WEILL POINT (0.5823, 0.2533) X_145 = ANTICOMPLEMENT OF NAGEL POINT (0.6735, 0.3333) X_942 = INCIRCLE-INVERSE OF X(36) (0.5878, 0.2633) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_3241 = REFLECTION OF X(2) IN X(1) (0.6054, 0.2666) X_78 = ISOGONAL CONJUGATE OF X(34) (0.3835, 0.0491) X_3243 = REFLECTION OF X(9) IN X(1) (0.6319, 0.3051) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.1429, 0.4666) X_3338 = INTERSECTION OF LINES X(1)X(3) AND X(7)X(90) (0.5971, 0.2805) X_3889 = com[INVERSE(n(3rd EULER TRIANGLE))] (0.6049, 0.2773) A B C X1 X21 X8 X354 X145 X942 X65 X3241 X78 X3243 X100 X3338 X3889 (a, b, c) = (5, 6, 7) | AB = 1

X3889 (X1656com[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 \(f(a,b,c) = a(b^{3} + c^{3} - a^{2}b - a^{2}c - 5abc)\)
Search Value (6, 9, 13): \(0.662639461257\)
▸ Linear Combinations1 combination
▸ Incident Central Lines16 lines

{1, 21}, {2, 3555}, {8, 354}, {65, 3241}, {72, 3622}, {78, 3243}, {100, 3338}, {145, 942}, {404, 3333}, {517, 3522}, {518, 3616}, {1125, 3681}, {1320, 3340}, {3218, 3295}, {3621, 3753}, {3633, 3754}