X₂₈₆₇

SM(X₁₀₇, X₁₁₀)

X₂₈₆₇ = intersection of antipedal lines of X₁₁₂ and X₁₂₉₇

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

X₂₈₆₇ (SM(X₁₀₇, X₁₁₀)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {112, 525}, {107, 850}

• Related Centers: X₂₈₈₁ (ISOGONAL CONJUGATE OF X₂₈₆₇), X₁₁₂ (Ψ(ORTHOCENTER, SYMMEDIAN POINT)), X₅₂₅ (ISOGONAL CONJUGATE OF X₁₁₂), X₁₀₇ (Ψ(SYMMEDIAN POINT, ORTHOCENTER)), X₈₅₀ (BARYCENTRIC MULTIPLIER FOR KIEPERT HYPERBOLA)

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where f(a,b,c) is given just before X₂₈₅₅ using P = X₁₀₇ and U = X₁₁₀

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

Search Value (6, 9, 13): \(2.985506713280\)

X₂₈₆₇ lies on the circumcircle.

▸ Incident Central Lines3 lines

{107, 850}, {112, 525}, {1297, 1503}

▸ Functional Relations3 relations

• X₂₈₆₇ = isogonal conjugate of X₂₈₈₁

• X₂₈₆₇ = anticomplement of X₃₃₅₀₄

• X₂₈₆₇ = intersection of antipedal lines of X₁₁₂ and X₁₂₉₇