X3396

SIN(A + 2π/5) POINT

X3396 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) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1139 = OUTER PENTAGON POINT (0.5970, 0.3096) 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_3396 = SIN(A + 2π/5) POINT (0.5378, 0.1645) A B C X1139 X3 X6 X2 X1140 X3396 (a, b, c) = (5, 6, 7) | AB = 1

X3396 (SIN(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 \(f(A,B,C) = \sin(A + 2\pi /5)\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(3.914336129552\)
▸ Incident Central Lines2 lines

{2, 1140}, {3, 6}

▸ Functional Relations5 relations