X₃₂₆₁

ISOTOMIC CONJUGATE OF X₁₀₁

X₃₂₆₁ is the isotomic conjugate of X₁₀₁.

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

X₃₂₆₁ (ISOTOMIC CONJUGATE OF X₁₀₁) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {75, 522}, {325, 523}

• Related Centers: X₁₀₁ (Ψ(INCENTER, SYMMEDIAN POINT)), X₇₅ (ISOTOMIC CONJUGATE OF INCENTER), X₅₂₂ (ISOGONAL CONJUGATE OF X₁₀₉), X₃₂₅ (-HIRST INVERSE OF X₆₉), X₅₂₃ (ISOGONAL CONJUGATE OF X₁₁₀)

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

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

Search Value (6, 9, 13): \(20.650275043246\)

▸ Incident Central Lines9 lines

{2, 2412}, {75, 522}, {86, 1459}, {99, 2690}, {100, 2860}, {325, 523}, {514, 1921}, {798, 802}, {824, 1577}

▸ Functional Relations13 relations

• X₃₂₆₁ = isogonal conjugate of X₃₂₇₃₉

• X₃₂₆₁ = isotomic conjugate of X₁₀₁

• X₃₂₆₁ = complement of X₂₁₂₂₅

• X₃₂₆₁ = anticomplement of X₆₅₈₆

• X₃₂₆₁ = X_i-Ceva conjugate of X_j for these (i,j): (561, 1111), (668, 1233), (670, 1269), (1978, 76)

• X₃₂₆₁ = cevapoint of X_i and X_j for these (i,j): (2, 150), (850, 1577)

• X₃₂₆₁ = X_i-cross conjugate of X_j for these (i,j): (116, 2), (1111, 561), (1577, 693), (1978, 76)

• X₃₂₆₁ = crosspoint of X₇₆ and X₁₉₇₈

• X₃₂₆₁ = crosssum of X_i and X_j for these (i,j): (32, 1919), (213, 3063), (1980, 2205)

• X₃₂₆₁ = crossdifference of every pair of points on the line X₃₂X₅₆₀

• X₃₂₆₁ = trilinear pole of line X₁₁₁₁X₃₁₂₀

• X₃₂₆₁ = pole wrt polar circle of trilinear polar of X₈₇₅₀ (line X₂₅X₄₁)

• X₃₂₆₁ = polar conjugate of X₈₇₅₀