X₃₃₈₈

CSC(A - π/8) POINT

X₃₃₈₈ and related points occupy Bernard Gibert’s Table 38. See the note at X₃₃₆₄.

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

X₃₃₈₈ (CSC(A - π/8) POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {5, 372}

• Related Centers: X₃₇₁ (KENMOTU POINT), X₃₃₈₇ (SEC(A - π/8) POINT), X₅ (NINE-POINT CENTER), X₃₇₂ ({X)

Trilinears: \(f(A,B,C) : f(B,C,A) : f(C,A,B)\), where \(f(A,B,C) = \csc(A - \pi /8)\)

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

Search Value (6, 9, 13): \(6.624678965734\)

X₃₃₈₈ lies on the Kiepert hyperbola.

▸ Incident Central Lines1 line

{5, 372}

▸ Functional Relations2 relations

• X₃₃₈₈ = isogonal conjugate of X₃₃₈₆

• X₃₃₈₈ = X₃₇₁-cross conjugate of X₃₃₈₇