X₈₃₁

o-(1, 3) CIRCUMCIRCLE POINT

X₈₃₁ = trilinear pole of line X₆X₃₈

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

X₈₃₁ (o-(1, 3) CIRCUMCIRCLE POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {662, 827}

• Related Centers: X₈₃₀ (ODD (1, 3) INFINITY POINT), X₆₆₂ (TRILINEAR POLE OF LINE X₁X₂₁), X₈₂₇ (o-(0, 4) CIRCUMCIRCLE POINT)

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = 1/[a^{0}(b^{3} - c^{3}) + a^{2}(b^{1} - c^{1})]\)

Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = af(a,b,c)\)

Search Value (6, 9, 13): \(2.269825801880\)

X₈₃₁ lies on the circumcircle.

▸ Incident Central Lines1 line

{662, 827}

▸ Functional Relations3 relations

• X₈₃₁ = isogonal conjugate of X₈₃₀

• X₈₃₁ = trilinear pole of line X₆X₃₈

• X₈₃₁ = Ψ(X₆, X₃₈)