X3868

X3com[INVERSE(n(3rd EULER TRIANGLE))]

X3868 = anticomplement of X72
< 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) { 7, 8 }: Gergonne–Nagel Line { 1, 21 }: Central Line L(1, 21) { 2, 72 }: Central Line L(2, 72) { 57, 78 }: Central Line L(57, 78) { 46, 100 }: Central Line L(46, 100) { 20, 145 }: Central Line L(20, 145) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2218 = -ISOCONJUGATE OF X(579) (-0.2871, -0.0657) X_7 = GERGONNE POINT (0.5903, 0.2769) 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_72 = ISOGONAL CONJUGATE OF X(28) (0.4367, 0.0733) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_78 = ISOGONAL CONJUGATE OF X(34) (0.3835, 0.0491) X_46 = -CEVA CONJUGATE OF X(1) (0.6917, 0.4543) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.1429, 0.4666) X_20 = DE LONGCHAMPS POINT (0.3878, -0.1916) X_145 = ANTICOMPLEMENT OF NAGEL POINT (0.6735, 0.3333) X_3868 = com[INVERSE(n(3rd EULER TRIANGLE))] (0.7388, 0.4532) A B C X2218 X7 X8 X1 X21 X2 X72 X57 X78 X46 X100 X20 X145 X3868 (a, b, c) = (5, 6, 7) | AB = 1

X3868 (X3com[INVERSE(n(3rd EULER TRIANGLE))]) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Barycentrics: \(a(b^{3} + c^{3} - a^{2}b - a^{2}c - abc)\)
Search Value (6, 9, 13): \(-3.448036731542\)
▸ Incident Central Lines63 lines

{1, 21}, {2, 72}, {3, 3218}, {4, 912}, {6, 977}, {7, 8}, {10, 3681}, {20, 145}, {27, 3187}, {34, 651}, {41, 3509}, {42, 986}, {46, 100}, {56, 1259}, {57, 78}, {84, 1320}, {101, 1729}, {144, 452}, {146, 149}, {171, 976}, {193, 1829}, {200, 3339}, {226, 2476}, {239, 379}, {244, 978}, {286, 2997}, {326, 1014}, {329, 938}, {354, 960}, {355, 2888}, {386, 3670}, {392, 3622}, {405, 3219}, {412, 1897}, {497, 1858}, {527, 950}, {579, 2198}, {580, 1331}, {596, 994}, {664, 3188}, {894, 964}, {908, 1210}, {936, 3306}, {971, 3146}, {982, 1193}, {997, 3338}, {1012, 1482}, {1445, 1467}, {1475, 3061}, {1490, 1998}, {1697, 3243}, {1698, 3678}, {1870, 1993}, {2095, 3149}, {2176, 3726}, {2280, 3496}, {2475, 2894}, {2802, 3633}, {2886, 3649}, {3057, 3241}, {3189, 3474}, {3617, 3753}, {3679, 3754}

▸ Functional Relations7 relations