X₂₄₂₇

ISOGONAL CONJUGATE OF X₂₄₀₁

X₂₄₂₇ is the isogonal conjugate of X₂₄₀₁.

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

X₂₄₂₇ (ISOGONAL CONJUGATE OF X₂₄₀₁) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {1, 6}, {101, 109}

• Related Centers: X₆₅₁ (TRILINEAR POLE OF LINE X₁X₃), X₉₀₁ (ISOGONAL CONJUGATE OF X₉₀₀), X₁ (INCENTER), X₆ (SYMMEDIAN POINT), X₁₀₁ (Ψ(INCENTER, SYMMEDIAN POINT)), X₁₀₉ (Ψ(INCENTER, CIRCUMCENTER))

Trilinears: \(1/f(a,b,c) : 1/f(b,c,a) : 1/f(c,a,b)\), where f(a,b,c) is as given just before X₂₃₉₄

Barycentrics: \(a/f(a,b,c) : b/f(b,c,a) : c/f(c,a,b)\)

Search Value (6, 9, 13): \(-1.208223143799\)

X₂₄₂₇ lies on the cubic K162.

▸ Incident Central Lines7 lines

{1, 6}, {101, 109}, {644, 1783}, {905, 1025}, {919, 2440}, {1110, 2426}, {2149, 2425}

▸ Functional Relations4 relations

• X₂₄₂₇ = isogonal conjugate of X₂₄₀₁

• X₂₄₂₇ = crosspoint of X₆₅₁ and X₉₀₁

• X₂₄₂₇ = crosssum of X₆₅₀ and X₉₀₀

• X₂₄₂₇ = crossdifference of every pair of points on line X₁₁X₅₁₃ (the Simson line of X₁₀₄)