X3379

COS(A - π/5) POINT

X3379 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 { 5, 1140 }: Central Line L(5, 1140) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3381 = SEC(A - π/5) POINT (0.5836, 0.2714) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_1140 = INNER PENTAGON POINT (0.5248, 1.3312) X_3379 = COS(A - π/5) POINT (0.5576, 0.1972) A B C X3381 X3 X6 X5 X1140 X3379 (a, b, c) = (5, 6, 7) | AB = 1

X3379 (COS(A - π/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 \(f(A,B,C) = \cos(A - \pi /5)\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(2.804833816450\)
▸ Incident Central Lines2 lines

{3, 6}, {5, 1140}

▸ Functional Relations4 relations