X3890

X3091com[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, 392 }: Central Line L(8, 392) { 145, 960 }: Central Line L(145, 960) { 517, 631 }: Central Line L(517, 631) { 100, 1697 }: Central Line L(100, 1697) { 986, 1149 }: Central Line L(986, 1149) 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_392 = X(1,6)∩X(10,11) (0.5265, 0.1800) X_145 = ANTICOMPLEMENT OF NAGEL POINT (0.6735, 0.3333) X_960 = INTERSECTION OF LINES X(1)X(6) AND X(5)X(10) (0.5041, 0.1533) X_517 = ISOGONAL CONJUGATE OF X(104) (0.8180, 0.7154) X_631 = 3/5*OG (0.5224, 0.1608) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.1429, 0.4666) X_1697 = INSIMILICENTER(BEVAN CIRCLE, INCIRCLE) (0.5449, 0.1845) X_986 = INTERSECTION OF LINES X(1)X(3) AND X(8)X(38) (0.5588, 0.2101) X_1149 = ISOGONAL CONJUGATE OF X(1120) (1.1667, 0.8165) X_3890 = com[INVERSE(n(3rd EULER TRIANGLE))] (0.5380, 0.1893) A B C X1 X21 X8 X392 X145 X960 X517 X631 X100 X1697 X986 X1149 X3890 (a, b, c) = (5, 6, 7) | AB = 1

X3890 (X3091com[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): \(2.717977557657\)
▸ Incident Central Lines15 lines

{1, 21}, {2, 3057}, {8, 392}, {65, 3622}, {72, 3241}, {100, 1697}, {145, 960}, {210, 3621}, {517, 631}, {518, 3623}, {986, 1149}, {1001, 2098}, {1698, 2802}, {3218, 3304}, {3633, 3678}