X3382

CSC(A - π/5) POINT

X3382 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) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3368 = COS(A - 2π/5) POINT (0.5852, 0.2428) X_3369 = SIN(A - 2π/5) POINT (0.3449, -0.1541) X_3382 = CSC(A - π/5) POINT (0.3759, 0.1017) A B C X3368 X3369 X3382 (a, b, c) = (5, 6, 7) | AB = 1

X3382 (CSC(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 \(f(A,B,C) = \csc(A - \pi /5)\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(-0.617219859551\)

X3382 lies on the Kiepert hyperbola.

▸ Functional Relations3 relations