X₂₈₃₁

ISOGONAL CONJUGATE OF X₂₇₄₇

X₂₈₃₁ is the isogonal conjugate of X₂₇₄₇.

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

X₂₈₃₁ (ISOGONAL CONJUGATE OF X₂₇₄₇) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {11, 132}, {104, 112}

• Related Centers: X₂₇₄₇ (SR(X₁₀₄, X₁₁₂)), X₁₁ (FEUERBACH POINT), X₁₃₂ (∩X₄X₃₂), X₁₀₄ (ANTIPODE OF X₁₀₀), X₁₁₂ (Ψ(ORTHOCENTER, SYMMEDIAN POINT))

Trilinears: \(1/f(a,b,c) : 1/f(b,c,a) : 1/f(c,a,b)\), where f(a,b,c) is as at X₂₇₄₇

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

▸ Incident Central Lines7 lines

{11, 132}, {30, 511}, {100, 1297}, {104, 112}, {119, 127}, {153, 322}, {1754, 1768}

▸ Functional Relations1 relation

• X₂₈₃₁ = isogonal conjugate of X₂₇₄₇