X3544

EULER LINE INTERCEPT OF LINE X6X_14842

< 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) { 2, 3 }: Euler Line { 3070, 3317 }: Central Line L(3070, 3317) { 3071, 3316 }: Central Line L(3071, 3316) { 3303, 3614 }: Central Line L(3303, 3614) { 3626, 3817 }: Central Line L(3626, 3817) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2 = CENTROID (0.5374, 0.2000) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_3070 = INTERSECTION OF X(4)X(6) AND X(5)X(372) (0.6043, 0.3120) X_3317 = ISOGONAL CONJUGATE OF X(3312) (0.4661, 0.1442) X_3071 = INTERSECTION OF X(4)X(6) AND X(5)X(371) (0.5859, 0.1197) X_3316 = ISOGONAL CONJUGATE OF X(3311) (0.5639, 0.2341) X_3303 = INTERSECTION OF LINES X(1)X(3) AND X(496)X(498) (0.5620, 0.2159) X_3614 = 1st HUTSON-FEUERBACH POINT (0.5602, 0.2447) X_3626 = H-1(X(1); M, -2) (0.4949, 0.1583) X_3817 = com(3rd EULER TRIANGLE) (0.5680, 0.2708) X_3544 = EULER LINE INTERCEPT OF LINE X(6)X(14842) (0.5594, 0.2575) A B C X2 X3 X3070 X3317 X3071 X3316 X3303 X3614 X3626 X3817 X3544 (a, b, c) = (5, 6, 7) | AB = 1

X3544 (EULER LINE INTERCEPT OF LINE X6X_14842) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Barycentrics: \(a^{4} + 8 a^{2} b^{2} - 9 b^{4} + 8 a^{2} c^{2} + 18 b^{2} c^{2} - 9 c^{4} : :\)
Search Value (6, 9, 13): \(0.186431085602\)
▸ Alternate Coordinates1 form

  • Barycentrics: \((2 a - b - c) (a^{2} (b + c) + 4 a (b^{2} - b c + c^{2}) + (b + c) (3 b^{2} - 8 b c + 3 c^{2})) : :\)

▸ Incident Central Lines154 lines

{2, 3}, {6, 14842}, {83, 39143}, {113, 15025}, {146, 15088}, {147, 15092}, {148, 38628}, {149, 38629}, {150, 38630}, {153, 38631}, {355, 20057}, {373, 6241}, {576, 11008}, {590, 23275}, {615, 23269}, {944, 7988}, {1056, 7741}, {1058, 7951}, {1131, 13951}, {1132, 8976}, {1285, 7746}, {1352, 22330}, {3070, 3317}, {3071, 3316}, {3244, 5587}, {3303, 3614}, {3304, 7173}, {3431, 18296}, {3448, 38632}, {3567, 27355}, {3590, 31487}, {3592, 23273}, {3594, 23267}, {3616, 38140}, {3617, 38034}, {3618, 33412}, {3620, 38136}, {3623, 38138}, {3626, 3817}, {3629, 10516}, {3631, 11477}, {3632, 5603}, {3636, 7967}, {3746, 10588}, {3982, 5714}, {4031, 9612}, {5158, 33630}, {5261, 10593}, {5274, 10592}, {5343, 16644}, {5344, 16645}, {5365, 16772}, {5366, 16773}, {5418, 12819}, {5420, 12818}, {5563, 10589}, {5881, 38076}, {5886, 32900}, {5889, 14845}, {5892, 11439}, {5943, 15058}, {6000, 11465}, {6154, 20400}, {6225, 32767}, {6329, 14912}, {6337, 15031}, {6361, 12571}, {6419, 13886}, {6420, 13939}, {6425, 23259}, {6426, 23249}, {6427, 18538}, {6428, 18762}, {6453, 32785}, {6454, 32786}, {6488, 9541}, {7317, 30323}, {7603, 7738}, {7612, 18843}, {7617, 14023}, {7687, 15034}, {7758, 8176}, {7772, 31415}, {7816, 39142}, {7991, 10175}, {8252, 10148}, {8253, 10147}, {8797, 32001}, {9624, 34627}, {9729, 16261}, {9779, 9956}, {9862, 38740}, {9955, 12245}, {10171, 18492}, {10222, 20050}, {10514, 26339}, {10515, 26340}, {11002, 11591}, {11017, 34783}, {11362, 30308}, {11451, 12162}, {11459, 16625}, {11482, 18358}, {11522, 34631}, {11695, 12290}, {12112, 37514}, {12244, 38729}, {12317, 15027}, {12383, 15044}, {12900, 15020}, {13172, 38751}, {13199, 38763}, {13452, 18418}, {13464, 34747}, {13472, 15077}, {14061, 35021}, {14094, 15081}, {14561, 22234}, {14639, 20399}, {14644, 20125}, {14651, 38745}, {14654, 38807}, {14683, 15046}, {15012, 15024}, {15018, 32139}, {15019, 15083}, {15029, 36253}, {15052, 36753}, {15054, 23515}, {15069, 20583}, {15808, 19925}, {16982, 23039}, {17852, 23251}, {18383, 35260}, {18424, 31652}, {18436, 18874}, {18439, 32205}, {18489, 18504}, {18493, 20054}, {18584, 31404}, {19872, 28150}, {19877, 22793}, {22681, 32522}, {23235, 36519}, {23513, 38669}, {23514, 38664}, {23516, 38683}, {28194, 30315}, {32815, 32887}, {32816, 32886}, {32823, 32868}, {32826, 37647}, {34641, 38021}, {36520, 38686}