X₂₈₅₇

SM(X₉₈, X₁₁₀)

X₂₈₅₇ = isogonal conjugate of X₂₈₇₁

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

X₂₈₅₇ (SM(X₉₈, X₁₁₀)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {112, 297}, {110, 325}

• Related Centers: X₂₈₇₁ (ISOGONAL CONJUGATE OF X₂₈₅₇), X₁₁₂ (Ψ(ORTHOCENTER, SYMMEDIAN POINT)), X₂₉₇ (-HIRST INVERSE OF X₄), X₁₁₀ (FOCUS OF KIEPERT PARABOLA), X₃₂₅ (-HIRST INVERSE OF X₆₉)

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 = X₉₈ and U = X₁₁₀

Barycentrics: \((a^{6} (b^{2} + c^{2}) - 2 a^{4} (b^{4} + c^{4}) + a^{2} (b^{6} + c^{6}) + b^{2} c^{2} (b^{2} - c^{2})^{2}) / (a^{6} (b^{2} + c^{2}) - a^{4} (b^{2} + c^{2})^{2} + a^{2} (b^{6} + c^{6}) - (b^{2} - c^{2})^{2} (b^{2} - b c + c^{2}) (b^{2} + b c + c^{2})) : :\)

Search Value (6, 9, 13): \(13.043209636744\)

X₂₈₅₇ lies on the circumcircle.

▸ Incident Central Lines5 lines

{2, 2715}, {98, 850}, {110, 325}, {112, 297}, {183, 476}

▸ Functional Relations3 relations

• X₂₈₅₇ = isogonal conjugate of X₂₈₇₁

• X₂₈₅₇ = anticomplement of X₃₈₉₇₅

• X₂₈₅₇ = orthoptic-circle-of-Steiner-inellipse-inverse of X₃₆₄₇₁