X₃₃₈₉

COS(A - π/12) POINT

X₃₃₈₉ and related points occupy Bernard Gibert’s Table 38. See the note at X₃₃₆₄.

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

X₃₃₈₉ (COS(A - π/12) POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {3, 6}, {13, 485}

• Related Centers: X₃₃₉₁ (SEC(A - π/12) POINT), X₃ (CIRCUMCENTER), X₆ (SYMMEDIAN POINT), X₁₃ (1st ISOGONIC CENTER), X₄₈₅ (VECTEN POINT)

Trilinears: \(\cos(A - \pi /12) : :\)

Search Value (6, 9, 13): \(4.192228949926\)

▸ Alternate Coordinates1 form

• Trilinears: \(\cos(A - \pi /3) - \sin(A - \pi /3) : :\)

▸ Incident Central Lines6 lines

{3, 6}, {13, 485}, {17, 590}, {18, 486}, {202, 1124}, {203, 2067}

▸ Functional Relations6 relations

• X₃₃₈₉ = isogonal conjugate of X₃₃₉₁

• X₃₃₈₉ = inverse-in-Brocard-circle of X₃₃₆₅

• X₃₃₈₉ = X₁₇-Ceva conjugate of X₃₃₉₀

• X₃₃₈₉ = X₃₂₀₅-cross conjugate of X₃₃₉₀

• X₃₃₈₉ = {X₁₆,X₆₁}-harmonic conjugate of X₃₃₉₀

• X₃₃₈₉ = {X₃₇₁,X₃₇₂}-harmonic conjugate of X₃₃₆₄