X₃₃₆₅

SIN(A - 5π/12) POINT

X₃₃₆₅ = X₁₈-Ceva conjugate of X₃₃₆₄

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

X₃₃₆₅ (SIN(A - 5π/12) POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {3, 6}, {14, 486}

• Related Centers: X₃₃₆₇ (CSC(A - 5π/12) POINT), X₃ (CIRCUMCENTER), X₆ (SYMMEDIAN POINT), X₁₄ (2nd ISOGONIC CENTER), X₄₈₆ (INNER VECTEN POINT)

Trilinears: \(\sin(A - 5\pi /12) : :\)

Search Value (6, 9, 13): \(31.397915105767\)

▸ Alternate Coordinates1 form

• Trilinears: cos(A + π/3) + sin(A + π/3) : :, X₃₃₆₅ and related points occupy Bernard Gibert’s Table 38. See the note at X₃₃₆₄.

▸ Incident Central Lines5 lines

{3, 6}, {14, 486}, {17, 485}, {18, 615}, {203, 1335}

▸ Functional Relations6 relations

• X₃₃₆₅ = isogonal conjugate of X₃₃₆₇

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

• X₃₃₆₅ = X₁₈-Ceva conjugate of X₃₃₆₄

• X₃₃₆₅ = X₃₂₀₆-cross conjugate of X₃₃₆₄

• X₃₃₆₅ = {X₁₅,X₆₂}-harmonic conjugate of X₃₃₆₄

• X₃₃₆₅ = {X₃₇₁,X₃₇₂}-harmonic conjugate of X₃₃₉₀