X₃₃₉₄

SIN(A + π/5) POINT

X₃₃₉₄ and related points occupy Bernard Gibert’s Table 38. See the note at X₃₃₆₄.

5, 6, 7 3, 4, 5 Kepler Kimberling

X₃₃₉₄ (SIN(A + π/5) POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {3, 6}

• Related Centers: X₃ (CIRCUMCENTER), X₆ (SYMMEDIAN POINT)

Trilinears: \(f(A,B,C) : f(B,C,A) : f(C,A,B)\), where \(f(A,B,C) = \sin(A + \pi /5)\)

Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)

Search Value (6, 9, 13): \(2.115192283337\)

▸ Incident Central Lines1 line

{3, 6}

▸ Functional Relations5 relations

• X₃₃₉₄ = isogonal conjugate of X₅₄₀₂

• X₃₃₉₄ = inverse-in-Brocard-circle of X₃₃₈₀

• X₃₃₉₄ = X₁₁₄₀-Ceva conjugate of X₃₃₉₃

• X₃₃₉₄ = crosspoint of X₁₁₃₉ and X₃₃₉₇

• X₃₃₉₄ = crosssum of X₃₃₉₅ and X₃₃₉₆