X3869

X3com[INVERSE(n(4th EULER TRIANGLE))]

X3869 = anticomplement of X65
< 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) { 4, 8 }: Fuhrmann Line { 1, 21 }: Central Line L(1, 21) { 2, 65 }: Central Line L(2, 65) { 40, 78 }: Central Line L(40, 78) { 144, 145 }: Central Line L(144, 145) { 46, 404 }: Central Line L(46, 404) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2217 = -ISOCONJUGATE OF X(573) (0.6164, 0.5653) X_4 = ORTHOCENTER (0.6122, 0.3958) X_8 = NAGEL POINT (0.4694, 0.1333) X_1 = INCENTER (0.5714, 0.2333) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_2 = CENTROID (0.5374, 0.2000) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_40 = BEVAN POINT (0.4286, -0.0292) X_78 = ISOGONAL CONJUGATE OF X(34) (0.3835, 0.0491) X_144 = ANTICOMPLEMENT OF X(7) (0.4317, 0.0461) X_145 = ANTICOMPLEMENT OF NAGEL POINT (0.6735, 0.3333) X_46 = -CEVA CONJUGATE OF X(1) (0.6917, 0.4543) X_404 = {X(2),X(3)}-HARMONIC CONJUGATE OF X(21) (0.5538, 0.2429) X_3869 = com[INVERSE(n(4th EULER TRIANGLE))] (0.4041, 0.0133) A B C X2217 X4 X8 X1 X21 X2 X65 X40 X78 X144 X145 X46 X404 X3869 (a, b, c) = (5, 6, 7) | AB = 1

X3869 (X3com[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 \(f(a,b,c) = a(b^{3} + c^{3} - a^{2}b - a^{2}c + abc)\)
Search Value (6, 9, 13): \(6.828653750456\)
▸ Incident Central Lines55 lines

{1, 21}, {2, 65}, {3, 3417}, {4, 8}, {6, 3727}, {9, 1405}, {10, 908}, {19, 2287}, {22, 3556}, {28, 1748}, {40, 78}, {41, 3496}, {46, 404}, {48, 1761}, {56, 3218}, {90, 1320}, {101, 1759}, {144, 145}, {146, 2778}, {210, 3617}, {213, 3735}, {219, 608}, {221, 394}, {314, 2995}, {354, 3622}, {391, 2262}, {392, 942}, {672, 3061}, {693, 1938}, {912, 944}, {934, 2365}, {936, 2093}, {956, 1482}, {958, 2099}, {982, 1201}, {986, 1193}, {995, 3670}, {1005, 1697}, {1156, 3680}, {1259, 3428}, {1610, 1812}, {1630, 2327}, {1698, 3754}, {1776, 2098}, {1836, 2475}, {1854, 3100}, {1898, 3621}, {2176, 3721}, {2390, 2979}, {2771, 3648}, {2802, 3632}, {3241, 3555}, {3306, 3339}, {3678, 3679}, {3698, 3740}

▸ Functional Relations7 relations