X₂₅₈₁

X₆-ISOCONJUGATE OF X₂₅₇₅

X₂₅₈₁ = isogonal conjugate of X₂₅₇₉

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

X₂₅₈₁ (X₆-ISOCONJUGATE OF X₂₅₇₅) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {19, 27}, {100, 1114}

• Related Centers: X₂₅₇₉ (-ISOCONJUGATE OF X₁₁₁₄), X₁₉ (CLAWSON POINT), X₂₇ (CEVAPOINT OF ORTHOCENTER AND CLAWSON CENTER), X₁₀₀ (ANTICOMPLEMENT OF FEUERBACH POINT), X₁₁₁₄ (2nd EULER-LINE-CIRCUMCIRCLE INTERSECTION)

Trilinears: \((1/a)f(a,b,c) : (1/b)f(b,c,a) : (1/c)/f(c,a,b)\), where f(a,b,c) is as at X₁₁₁₄

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

Search Value (6, 9, 13): \(7.161938433500\)

▸ Incident Central Lines8 lines

{19, 27}, {100, 1114}, {162, 1823}, {240, 2586}, {662, 2577}, {897, 2588}, {1821, 2578}, {2349, 2582}

▸ Functional Relations6 relations

• X₂₅₈₁ = isogonal conjugate of X₂₅₇₉

• X₂₅₈₁ = isotomic conjugate of X₂₅₈₃

• X₂₅₈₁ = cevapoint of X_i and X_j for these (i,j): (1, 2579), (19, 2589), (63, 2583), (1823, 2577)

• X₂₅₈₁ = crosssum of X_i and X_j for these (i,j): (1577, 2580), (2577, 2587), (2589, 75)

• X₂₅₈₁ = X_i-cross conjugate of X_j for these (i,j): (2579, 1), (2583, 92)

• X₂₅₈₁ = X₁₁₁₄-aleph conjugate of X₁₇₄₀