X3816

X57com(3rd EULER TRIANGLE)

X3816 = complement of X1376
< 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, 1376 }: Central Line L(2, 1376) { 2, 11 }: Central Line L(2, 11) { 10, 496 }: Central Line L(10, 496) { 5, 515 }: Central Line L(5, 515) { 405, 499 }: Central Line L(405, 499) 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_1376 = EXSIMILICENTER(CIRCUMCIRCLE, SPIEKER CIRCLE) (0.5265, 0.2074) X_11 = FEUERBACH POINT (0.7347, 0.0667) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_496 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(495) (0.5843, 0.2201) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_515 = ISOGONAL CONJUGATE OF X(102) (0.6804, 0.7691) X_405 = EULER LINE INTERCEPT OF LINE X(1)X(6) (0.5325, 0.1870) X_499 = {X(1),X(2)}-HARMONIC CONJUGATE OF X(498) (0.4458, 0.1102) X_3816 = com(3rd EULER TRIANGLE) (0.5429, 0.1963) A B C Ma Mb Mc X2 X1376 X11 X10 X496 X5 X515 X405 X499 X3816 (a, b, c) = (5, 6, 7) | AB = 1

X3816 (X57com(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, 1376}

  • Related Centers: X2 (CENTROID), X1376 (EXSIMILICENTER)

Barycentrics: \((b^{2}-4 b c+c^{2}) a-(b+c) \cdot (b-c)^{2} : :\)
Search Value (6, 9, 13): \(2.631482432997\)
▸ Incident Central Lines25 lines

{1, 1329}, {2, 11}, {5, 515}, {8, 1997}, {10, 496}, {12, 1388}, {38, 1647}, {56, 2478}, {142, 1538}, {226, 3660}, {354, 908}, {392, 1737}, {405, 499}, {442, 3586}, {474, 1479}, {495, 551}, {518, 3452}, {529, 999}, {958, 3086}, {960, 1210}, {978, 1834}, {982, 3756}, {1532, 3576}, {1836, 3306}, {3304, 3436}

▸ Functional Relations1 relation