X₃₃₇₃

SEC(A - 3π/8) POINT

X₃₃₇₃ and related points occupy Bernard Gibert’s Table 38. See the note at X₃₃₆₄.

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

X₃₃₇₃ (SEC(A - 3π/8) POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {5, 371}

• Related Centers: X₃₇₂ ({X), X₃₃₇₄ (CSC(A - 3π/8) POINT), X₅ (NINE-POINT CENTER), X₃₇₁ (KENMOTU POINT)

Trilinears: \(\sec(A - 3\pi /8) : :\)

Search Value (6, 9, 13): \(1.656403335237\)

▸ Alternate Coordinates1 form

• Trilinears: \(\csc(A + \pi /8) : :\)

X₃₃₇₃ lies on the Kiepert hyperbola.

▸ Incident Central Lines1 line

{5, 371}

▸ Functional Relations2 relations

• X₃₃₇₃ = isogonal conjugate of X₃₃₇₁

• X₃₃₇₃ = X₃₇₂-cross conjugate of X₃₃₇₄