X1586

POINT CAPH II

X1586 = polar conjugate of X486
< A B C >: Reference Triangle △ABC [ A B ]: Sideline AB (Base c = 1) [ B C ]: Sideline BC (Side a) [ C A ]: Sideline CA (Side b) { 2, 3 }: Euler Line { 53, 615 }: Central Line L(53, 615) { 264, 494 }: Central Line L(264, 494) { 317, 491 }: Central Line L(317, 491) { 393, 494 }: Central Line L(393, 494) { 343, 637 }: Central Line L(343, 637) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2 = CENTROID (0.5374, 0.2000) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_4 = ORTHOCENTER (0.6122, 0.3958) X_53 = SYMMEDIAN POINT OF ORTHIC TRIANGLE (0.6164, 0.4390) X_615 = ISOGONAL CONJUGATE OF X(589) (0.4337, 0.0885) X_264 = ISOTOMIC CONJUGATE OF CIRCUMCENTER (0.5720, 0.3293) X_494 = 2nd VAN LAMOEN HOMOTHETIC CENTER (0.8529, 0.5391) X_317 = ISOTOMIC CONJUGATE OF X(68) (0.6796, 0.5070) X_491 = CEVAPOINT OF X(2) AND X(487) (0.7449, 0.4229) X_393 = -CROSS CONJUGATE OF X(4) (0.6247, 0.5263) X_343 = ISOTOMIC CONJUGATE OF X(275) (0.4345, 0.0893) X_637 = ANTICOMPLEMENT OF X(371) (0.4819, 0.1805) X_1586 = POINT CAPH II (0.6630, 0.5285) A B C X2 X3 X4 X53 X615 X264 X494 X317 X491 X393 X343 X637 X1586 (a, b, c) = (5, 6, 7) | AB = 1

X1586 (POINT CAPH II) 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 \(f(A,B,C) = \csc A - \sec A\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(1.216996902611\)
▸ Incident Central Lines8 lines

{2, 3}, {53, 615}, {264, 494}, {317, 491}, {343, 637}, {393, 494}, {394, 638}, {489, 1322}

▸ Functional Relations4 relations

Notes

As a point on the Euler line, X1586 has Shinagawa coefficients \((F, -S)\).