X3885

X1com[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) { 1, 88 }: Central Line L(1, 88) { 20, 145 }: Central Line L(20, 145) { 8, 210 }: Central Line L(8, 210) { 149, 355 }: Central Line L(149, 355) { 496, 1145 }: Central Line L(496, 1145) { 21, 1697 }: Central Line L(21, 1697) 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_88 = ISOGONAL CONJUGATE OF X(44) (1.0000, 0.0000) X_20 = DE LONGCHAMPS POINT (0.3878, -0.1916) X_145 = ANTICOMPLEMENT OF NAGEL POINT (0.6735, 0.3333) X_8 = NAGEL POINT (0.4694, 0.1333) X_210 = -CEVA CONJUGATE OF X(37) (0.4925, 0.1466) X_149 = REFLECTION OF X(20) IN X(104) (1.3265, -0.3333) X_355 = FUHRMANN CENTER (0.5408, 0.2645) X_496 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(495) (0.5843, 0.2201) X_1145 = 3rd EHRMANN POINT (0.3061, 0.2999) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_1697 = INSIMILICENTER(BEVAN CIRCLE, INCIRCLE) (0.5449, 0.1845) X_3885 = com[INVERSE(n(4th EULER TRIANGLE))] (0.6082, 0.2133) A B C X1 X88 X20 X145 X8 X210 X149 X355 X496 X1145 X21 X1697 X3885 (a, b, c) = (5, 6, 7) | AB = 1

X3885 (X1com[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 \(f(a,b,c) = a(b + c - a)(b^{2} + c^{2} + ab + ac - 3bc)\)
Search Value (6, 9, 13): \(1.194292052266\)
▸ Linear Combinations1 combination
▸ Incident Central Lines18 lines

{1, 88}, {8, 210}, {20, 145}, {21, 1697}, {65, 3241}, {72, 3621}, {78, 2136}, {149, 355}, {392, 3617}, {496, 1145}, {518, 3644}, {644, 2082}, {758, 3633}, {942, 3623}, {1482, 3149}, {2170, 3208}, {3622, 3753}, {3632, 3681}