X3811

X3189com(EULER TRIANGLE)

X3811 = intouch-to-ABC barycentric image of X3
< 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, 2 }: Nagel Line { 35, 63 }: Central Line L(35, 63) { 55, 72 }: Central Line L(55, 72) { 46, 100 }: Central Line L(46, 100) { 3, 518 }: Central Line L(3, 518) { 210, 405 }: Central Line L(210, 405) 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_2 = CENTROID (0.5374, 0.2000) X_35 = {X(1),X(3)}-HARMONIC CONJUGATE OF X(36) (0.5373, 0.1706) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4566, 0.0823) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_72 = ISOGONAL CONJUGATE OF X(28) (0.4367, 0.0733) X_46 = -CEVA CONJUGATE OF X(1) (0.6917, 0.4543) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.1429, 0.4666) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_518 = ISOGONAL CONJUGATE OF X(105) (0.9154, 0.6489) X_210 = -CEVA CONJUGATE OF X(37) (0.4925, 0.1466) X_405 = EULER LINE INTERCEPT OF LINE X(1)X(6) (0.5325, 0.1870) X_3811 = com(EULER TRIANGLE) (0.7946, 0.4520) A B C X1 X2 X35 X63 X55 X72 X46 X100 X3 X518 X210 X405 X3811 (a, b, c) = (5, 6, 7) | AB = 1

X3811 (X3189com(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 \(f(a,b,c) = a(a^{3} + b^{3} + c^{3} - a^{2}b - ab^{2} - a^{2}c - ac^{2} + b^{2}c + bc^{2} - 2abc)\)
Search Value (6, 9, 13): \(-10.670072465948\)
▸ Incident Central Lines53 lines

{1, 2}, {3, 518}, {4, 2900}, {6, 3694}, {9, 943}, {12, 3419}, {21, 3681}, {33, 2901}, {35, 63}, {37, 2271}, {40, 758}, {46, 100}, {47, 1331}, {55, 72}, {56, 3555}, {58, 1792}, {65, 3689}, {84, 2801}, {101, 1973}, {158, 1897}, {169, 3684}, {210, 405}, {214, 1420}, {218, 3693}, {354, 474}, {392, 3303}, {404, 3338}, {443, 3475}, {500, 524}, {516, 1490}, {595, 3749}, {726, 990}, {908, 1479}, {912, 1158}, {942, 1376}, {954, 3059}, {956, 2646}, {960, 3295}, {993, 3601}, {1046, 3550}, {1066, 1818}, {1389, 3680}, {1612, 1723}, {1706, 3754}, {2136, 2802}, {2177, 2292}, {2321, 3553}, {2550, 3487}, {2551, 3488}, {2975, 3612}, {3243, 3333}, {3421, 3486}, {3697, 3711}

▸ Functional Relations1 relation

  • X3811 = intouch-to-ABC barycentric image of X3