X₃₂₆₆

ISOTOMIC CONJUGATE OF X₁₁₁

X₃₂₆₆ is the isotomic conjugate of X₁₁₁.

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

X₃₂₆₆ (ISOTOMIC CONJUGATE OF X₁₁₁) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {2, 39}, {23, 99}

• Related Centers: X₁₁₁ (PARRY POINT), X₂ (CENTROID), X₃₉ (BROCARD MIDPOINT), X₂₃ (FAR-OUT POINT), X₉₉ (STEINER POINT)

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = (2a^{2} - b^{2} - c^{2})/a^{3}\)

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

Search Value (6, 9, 13): \(9.358419928057\)

▸ Incident Central Lines6 lines

{2, 39}, {23, 99}, {98, 2858}, {110, 2868}, {325, 523}, {1975, 1995}

▸ Functional Relations7 relations

• X₃₂₆₆ = isogonal conjugate of X₃₂₇₄₀

• X₃₂₆₆ = isotomic conjugate of X₁₁₁

• X₃₂₆₆ = anticomplement of X₃₂₉₁

• X₃₂₆₆ = trilinear pole of line X₆₉₀X₅₁₈₁

• X₃₂₆₆ = pole wrt polar circle of trilinear polar of X₈₇₅₃ (X₂₅X₂₄₈₉)

• X₃₂₆₆ = polar conjugate of X₈₇₅₃

• X₃₂₆₆ = crossdifference of every pair of points on line X₃₂X₆₆₉