X3006

(DE LONGCHAMPS LINE)∩(NAGEL LINE)

X3006 = anticomplement of X3011
< A B C >: Reference Triangle △ABC < K_a K_b K_c >: Anticomplementary Triangle △K_a K_b K_c [ A B ]: Sideline AB (Base c = 1) [ B C ]: Sideline BC (Side a) [ C A ]: Sideline CA (Side b) { 2, 3011 }: Nagel Line { 1, 2 }: Nagel Line { 325, 523 }: Central Line L(325, 523) { 752, 896 }: Central Line L(752, 896) { 38, 2887 }: Central Line L(38, 2887) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) K_a = Anticomplementary Vertex K_a (1.6122, 0.5999) K_b = Anticomplementary Vertex K_b (-0.3878, 0.5999) K_c = Anticomplementary Vertex K_c (0.3878, -0.5999) X_2 = CENTROID (0.5374, 0.2000) X_3011 = (NAGEL LINE)∩(ORTHIC AXIS) (1.0051, 0.6582) X_1 = INCENTER (0.5714, 0.2333) X_325 = -HIRST INVERSE OF X(69) (-0.3370, -0.7398) X_523 = ISOGONAL CONJUGATE OF X(110) (1.0856, -0.0096) X_752 = EVEN (0, 3) INFINITY POINT (0.9166, 0.6478) X_896 = INTERSECTION OF LINES X(1)X(21) AND X(9)X(750) (2.0357, 2.1579) X_38 = CROSSPOINT OF X(1) AND X(75) (0.5443, 0.1976) X_2887 = COMPLEMENTARY CONJUGATE OF X(37) (0.4947, 0.1495) X_3006 = (DE LONGCHAMPS LINE)∩(NAGEL LINE) (-0.3980, -0.7165) A B C Ka Kb Kc X2 X3011 X1 X325 X523 X752 X896 X38 X2887 X3006 (a, b, c) = (5, 6, 7) | AB = 1

X3006 ((DE LONGCHAMPS LINE)∩(NAGEL LINE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = bc(b^{3} + c^{3} - ab^{2} - ac^{2})\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(7.932609093277\)
▸ Incident Central Lines5 lines

{1, 2}, {38, 2887}, {321, 2886}, {325, 523}, {752, 896}

▸ Functional Relations2 relations