X638

ANTICOMPLEMENT OF X372

X638 is the anticomplement of X372.
< 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, 372 }: Central Line L(2, 372) { 4, 69 }: Central Line L(4, 69) { 3, 490 }: Central Line L(3, 490) { 5, 492 }: Central Line L(5, 492) { 20, 487 }: Central Line L(20, 487) 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_372 = {X(3),X(6)}-HARMONIC CONJUGATE OF X(371) (0.7148, 0.4568) X_4 = ORTHOCENTER (0.6122, 0.3958) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.4122, 0.0654) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_490 = CEVAPOINT OF X(20) AND X(488) (0.4037, -0.0241) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_492 = CEVAPOINT OF X(2) AND X(488) (0.4893, 0.1483) X_20 = DE LONGCHAMPS POINT (0.3878, -0.1916) X_487 = ANTICOMPLEMENT OF X(486) (1.7742, 0.6338) X_638 = ANTICOMPLEMENT OF X(372) (0.1827, -0.3137) A B C Ka Kb Kc X2 X372 X4 X69 X3 X490 X5 X492 X20 X487 X638 (a, b, c) = (5, 6, 7) | AB = 1

X638 (ANTICOMPLEMENT OF X372) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

  • Derived Triangle: Anticomplementary Triangle △KaKbKc — vertices Ka, Kb, Kc (Formed by lines through A, B, C parallel to opposite sides)

  • Central Lines: {2, 372}

  • Related Centers: X2 (CENTROID), X372 ({X)

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = (S_{B}S_{C} - 2S_{A} \operatorname{area})/a\)
Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = af(a,b,c)\)
Search Value (6, 9, 13): \(11.630377459613\)
▸ Incident Central Lines6 lines

{2, 372}, {3, 490}, {4, 69}, {5, 492}, {20, 487}, {30, 489}

▸ Functional Relations3 relations