X490

CEVAPOINT OF X20 AND X488

X490 is the cevapoint of X20 and X488.
< 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, 3070 }: Central Line L(2, 3070) { 20, 64 }: Central Line L(20, 64) { 4, 488 }: Central Line L(4, 488) { 376, 487 }: Central Line L(376, 487) { 3, 491 }: Central Line L(3, 491) 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_3070 = INTERSECTION OF X(4)X(6) AND X(5)X(372) (0.6043, 0.3120) X_20 = DE LONGCHAMPS POINT (0.3878, -0.1916) X_64 = ISOGONAL CONJUGATE OF X(20) (0.5579, 1.5943) X_4 = ORTHOCENTER (0.6122, 0.3958) X_488 = ANTICOMPLEMENT OF X(485) (0.4576, 0.0844) X_376 = CENTROID OF THE ANTIPEDAL TRIANGLE OF X(2) (0.4626, 0.0042) X_487 = ANTICOMPLEMENT OF X(486) (1.7742, 0.6338) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_491 = CEVAPOINT OF X(2) AND X(487) (0.7449, 0.4229) X_490 = CEVAPOINT OF X(20) AND X(488) (0.4037, -0.0241) A B C Ka Kb Kc X2 X3070 X20 X64 X4 X488 X376 X487 X3 X491 X490 (a, b, c) = (5, 6, 7) | AB = 1

X490 (CEVAPOINT OF X20 AND X488) 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 \(f(A,B,C) = (\cos A)(1 + \csc A \sin B \sin C) - \cos B \cos C\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(9.219285468823\)
▸ Incident Central Lines7 lines

{3, 491}, {4, 488}, {20, 64}, {30, 637}, {175, 664}, {376, 487}, {486, 671}

▸ Functional Relations3 relations

Notes

X490 is a perspector of triangles associated with squares that circumscribe ABC. For details and reference, see X488. (Floor van Lamoen, 4/29/98)