X₂₇₆₄

SR(X₁₀₇, X₁₁₂)

X₂₇₆₄ = Λ(X₁₀₇, X₁₁₂)

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

X₂₇₆₄ (SR(X₁₀₇, X₁₁₂)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {107, 525}, {112, 520}

• Related Centers: X₂₈₄₈ (ISOGONAL CONJUGATE OF X₂₇₆₄), X₁₀₇ (Ψ(SYMMEDIAN POINT, ORTHOCENTER)), X₅₂₅ (ISOGONAL CONJUGATE OF X₁₁₂), X₁₁₂ (Ψ(ORTHOCENTER, SYMMEDIAN POINT)), X₅₂₀ (ISOGONAL CONJUGATE OF X₁₀₇)

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where f(a,b,c) is as given just before X₂₆₇₇ using P = X₁₀₇, U = X₁₁₂

Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)

Search Value (6, 9, 13): \(2.085784469077\)

X₂₇₆₄ lies on the circumcircle.

▸ Incident Central Lines4 lines

{107, 525}, {112, 520}, {1294, 1503}, {2435, 2442}

▸ Functional Relations2 relations

• X₂₇₆₄ = isogonal conjugate of X₂₈₄₈

• X₂₇₆₄ = Λ(X₁₀₇, X₁₁₂)