X₃₂₆₀

ISOTOMIC CONJUGATE OF X₇₄

X₃₂₆₀ is the isotomic conjugate of X₇₄.

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

X₃₂₆₀ (ISOTOMIC CONJUGATE OF X₇₄) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Derived Triangle: Anticomplementary Triangle △K_aK_bK_c — vertices K_a, K_b, K_c (Formed by lines through A, B, C parallel to opposite sides)

• Central Lines: {2, 3003}

• Related Centers: X₂ (CENTROID), X₃₀₀₃ ((BROCARD AXIS)∩(ORTHIC AXIS))

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = b^{2}c^{2}(\cos A - 2 \cos B \cos C)\)

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

Search Value (6, 9, 13): \(6.960872719970\)

▸ Incident Central Lines13 lines

{4, 69}, {94, 323}, {98, 2855}, {99, 477}, {183, 1995}, {290, 892}, {298, 300}, {298, 301}, {324, 394}, {325, 523}, {328, 1494}, {338, 524}, {1138, 1272}

▸ Functional Relations10 relations

• X₃₂₆₀ = isotomic conjugate of X₇₄

• X₃₂₆₀ = anticomplement of X₃₀₀₃

• X₃₂₆₀ = X₃₂₈-Ceva conjugate of X₃₁₁

• X₃₂₆₀ = cevapoint of X_i and X_j for these (i,j): (2, 146), (69, 1272), (323, 2071)

• X₃₂₆₀ = X₁₁₃-cross conjugate of X₂

• X₃₂₆₀ = crosspoint of X₃₀₀ and X₃₀₁

• X₃₂₆₀ = crossdifference of every pair of points on the line X₃₂X₃₀₄₉

• X₃₂₆₀ = trilinear pole of line X₁₆₃₇X₅₆₆₄

• X₃₂₆₀ = pole wrt polar circle of trilinear polar of X₈₇₄₉ (line X₂₅X₅₁₂)

• X₃₂₆₀ = polar conjugate of X₈₇₄₉