X3368

COS(A - 2π/5) POINT

X3368 and related points occupy Bernard Gibert’s Table 38. See the note at X3364.
< 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) { 3, 6 }: Brocard Axis { 2, 1140 }: Central Line L(2, 1140) { 4, 1139 }: Central Line L(4, 1139) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3370 = SEC(A - 2π/5) POINT (0.5569, 0.2237) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_2 = CENTROID (0.5374, 0.2000) X_1140 = INNER PENTAGON POINT (0.5248, 1.3312) X_4 = ORTHOCENTER (0.6122, 0.3958) X_1139 = OUTER PENTAGON POINT (0.5970, 0.3096) X_3368 = COS(A - 2π/5) POINT (0.5852, 0.2428) A B C X3370 X3 X6 X2 X1140 X4 X1139 X3368 (a, b, c) = (5, 6, 7) | AB = 1

X3368 (COS(A - 2π/5) POINT) 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 \(f(A,B,C) = \cos(A - 2\pi /5)\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(1.555046324366\)
▸ Incident Central Lines3 lines

{2, 1140}, {3, 6}, {4, 1139}

▸ Functional Relations4 relations