X3846

X1999com(3rd EULER TRIANGLE)

X3846 = complement of X171
< A B C >: Reference Triangle △ABC < M_a M_b M_c >: Medial Triangle △M_a M_b M_c [ A B ]: Sideline AB (Base c = 1) [ B C ]: Sideline BC (Side a) [ C A ]: Sideline CA (Side b) { 2, 171 }: Central Line L(2, 171) { 5, 10 }: Central Line L(5, 10) { 2, 31 }: Central Line L(2, 31) { 114, 124 }: Central Line L(114, 124) { 11, 1211 }: Central Line L(11, 1211) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) M_a = Midpoint M_a of BC (0.8061, 0.2999) M_b = Midpoint M_b of CA (0.3061, 0.2999) M_c = Midpoint M_c of AB (0.5000, 0.0000) X_2 = CENTROID (0.5374, 0.2000) X_171 = {X(2), X(31)}-HARMONIC CONJUGATE OF X(238) (0.5819, 0.2525) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_114 = KIEPERT ANTIPODE (0.3616, 0.4140) X_124 = -OF-MEDIAL-TRIANGLE (0.6243, 0.0030) X_11 = FEUERBACH POINT (0.7347, 0.0667) X_1211 = ISOGONAL CONJUGATE OF X(1169) (0.5137, 0.1744) X_3846 = com(3rd EULER TRIANGLE) (0.5152, 0.1737) A B C Ma Mb Mc X2 X171 X5 X10 X31 X114 X124 X11 X1211 X3846 (a, b, c) = (5, 6, 7) | AB = 1

X3846 (X1999com(3rd EULER TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

  • Derived Triangle: Medial Triangle △MaMbMc — vertices Ma, Mb, Mc (Formed by the midpoints of sides BC, CA, AB)

  • Central Lines: {2, 171}

  • Related Centers: X2 (CENTROID), X171 ({X)

Barycentrics: \(b^{3} + c^{3} + 2abc : :\)
Search Value (6, 9, 13): \(3.254144494515\)
▸ Incident Central Lines104 lines

{2, 31}, {5, 10}, {9, 4438}, {11, 1211}, {42, 5741}, {43, 4085}, {57, 4655}, {63, 4703}, {75, 3944}, {114, 124}, {141, 3816}, {142, 4138}, {226, 24325}, {244, 17184}, {312, 3773}, {325, 4357}, {612, 4865}, {726, 4415}, {740, 3687}, {756, 3006}, {899, 4972}, {908, 1215}, {978, 16062}, {984, 3705}, {1001, 3771}, {1100, 10026}, {1104, 1125}, {1193, 5051}, {1203, 25441}, {1376, 4660}, {1836, 3980}, {1921, 7018}, {1999, 17772}, {3120, 4359}, {3178, 6051}, {3218, 4683}, {3266, 21415}, {3662, 17063}, {3666, 4425}, {3670, 14815}, {3702, 20653}, {3703, 3971}, {3706, 21085}, {3717, 4096}, {3720, 3936}, {3727, 4167}, {3739, 3838}, {3752, 3821}, {3757, 17719}, {3772, 16825}, {3782, 24165}, {3831, 4187}, {3834, 3848}, {3844, 11814}, {3923, 24703}, {3925, 5241}, {3931, 17748}, {3961, 4514}, {3966, 4362}, {4011, 4679}, {4023, 4685}, {4026, 6685}, {4038, 17778}, {4104, 4847}, {4199, 21321}, {4358, 15523}, {4383, 25453}, {4384, 17064}, {4389, 17591}, {4418, 5057}, {4429, 16569}, {4647, 6042}, {4854, 4970}, {4892, 5249}, {5015, 5293}, {5211, 17598}, {5259, 25645}, {5272, 25527}, {5278, 24892}, {5739, 11269}, {5814, 17733}, {5955, 12699}, {7741, 10479}, {7988, 18229}, {8167, 16846}, {9284, 16584}, {10453, 24217}, {11680, 21242}, {15507, 18235}, {15825, 19863}, {16610, 24169}, {16739, 17203}, {16817, 24161}, {17202, 23659}, {17234, 25502}, {17274, 18193}, {17355, 17747}, {17357, 21249}, {17596, 24723}, {17605, 25385}, {17889, 19804}, {19543, 25440}, {19563, 20333}, {21856, 25066}

▸ Functional Relations3 relations