X₂₇₄₉

SR(X₁₀₅, X₁₀₇)

X₂₇₄₉ = isogonal conjugate of X₂₈₃₃

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

X₂₇₄₉ (SR(X₁₀₅, X₁₀₇)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {105, 520}, {107, 518}

• Related Centers: X₂₈₃₃ (ISOGONAL CONJUGATE OF X₂₇₄₉), X₁₀₅ (Λ(INCENTER, SYMMEDIAN POINT)), X₅₂₀ (ISOGONAL CONJUGATE OF X₁₀₇), X₁₀₇ (Ψ(SYMMEDIAN POINT, ORTHOCENTER)), X₅₁₈ (ISOGONAL CONJUGATE OF X₁₀₅)

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 = X₁₀₅, U = X₁₀₇

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

Search Value (6, 9, 13): \(11.239037411264\)

X₂₇₄₉ lies on the circumcircle.

▸ Incident Central Lines2 lines

{105, 520}, {107, 518}

▸ Functional Relations1 relation

• X₂₇₄₉ = isogonal conjugate of X₂₈₃₃