X3960

X676com(HEXYL TRIANGLE)

X3960 = complement of X3762
< 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, 3762 }: Central Line L(2, 3762) { 104, 106 }: Central Line L(104, 106) { 101, 651 }: Central Line L(101, 651) { 241, 514 }: Central Line L(241, 514) { 659, 764 }: Central Line L(659, 764) 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_3762 = com[T(bc, c2)] (-1.5306, -1.4997) X_104 = ANTIPODE OF X(100) (0.8571, -0.2624) X_106 = Λ(INCENTER, CENTROID) (1.0000, 0.0000) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.2143, 0.5249) X_651 = TRILINEAR POLE OF LINE X(1)X(3) (0.3048, 0.5599) X_241 = -LINE CONJUGATE OF X(55) (1.1217, 1.2442) X_514 = ISOGONAL CONJUGATE OF X(101) (1.0761, -0.0329) X_659 = CROSSDIFFERENCE OF X(1) AND X(39) (1.9286, 2.2162) X_764 = TRILINEAR CUBE OF X(513) (1.2143, -0.1166) X_3960 = com(HEXYL TRIANGLE) (1.5714, 1.0498) A B C Ma Mb Mc X2 X3762 X104 X106 X101 X651 X241 X514 X659 X764 X3960 (a, b, c) = (5, 6, 7) | AB = 1

X3960 (X676com(HEXYL 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, 3762}

  • Related Centers: X2 (CENTROID), X3762 (com[T(bc, c2)])

Barycentrics: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = a(b - c)(b^{2} + c^{2} - a^{2} - bc)\)
Search Value (6, 9, 13): \(-3.903807748032\)
▸ Incident Central Lines18 lines

{1, 2254}, {2, 3762}, {3, 2814}, {88, 1022}, {101, 651}, {104, 106}, {214, 3738}, {241, 514}, {513, 1960}, {659, 764}, {667, 3777}, {676, 2826}, {690, 3743}, {812, 1015}, {830, 2530}, {900, 1387}, {1125, 3716}, {2006, 2401}

▸ Functional Relations4 relations