X₃₃₆₉

SIN(A - 2π/5) POINT

X₃₃₆₉ and related points occupy Bernard Gibert’s Table 38. See the note at X₃₃₆₄.

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

X₃₃₆₉ (SIN(A - 2π/5) POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {3, 6}, {2, 1139}

• Related Centers: X₁₁₄₀ (INNER PENTAGON POINT), X₃ (CIRCUMCENTER), X₆ (SYMMEDIAN POINT), X₂ (CENTROID), X₁₁₃₉ (OUTER PENTAGON POINT)

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): \(317.719435989633\)

▸ Incident Central Lines2 lines

{2, 1139}, {3, 6}

▸ Functional Relations5 relations

• X₃₃₆₉ = isogonal conjugate of X₁₁₄₀

• X₃₃₆₉ = {X₃₇₁,X₃₇₂}-harmonic conjugate of X₃₃₉₅

• X₃₃₆₉ = inverse-in-Brocard-circle of X₃₃₉₆

• X₃₃₆₉ = X₃₃₈₂-Ceva conjugate of X₃₃₆₈

• X₃₃₆₉ = crosssum of X₃₃₉₃ and X₃₃₉₄