X₃₃₈₅

COS(A - π/8) POINT

X₃₃₈₅ and related points occupy Bernard Gibert’s Table 38. See the note at X₃₃₆₄.

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

X₃₃₈₅ (COS(A - π/8) 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: X₃₃₈₇ (SEC(A - π/8) POINT), X₃ (CIRCUMCENTER), X₆ (SYMMEDIAN POINT)

Trilinears: \(\cos(A - \pi /8)\)

Search Value (6, 9, 13): \(3.564267023208\)

▸ Incident Central Lines1 line

{3, 6}

▸ Functional Relations5 relations

• X₃₃₈₅ = isogonal conjugate of X₃₃₈₇

• X₃₃₈₅ = inverse-in-Brocard-circle of X₃₃₇₂

• X₃₃₈₅ = X₄₈₅-Ceva conjugate of X₃₃₈₆

• X₃₃₈₅ = insimilicenter of circumcircle and 1st Kenmotu circle

• X₃₃₈₅ = {X₃₇₁,X₃₇₂}-harmonic conjugate of X₃₃₇₁