X₂₅₈₈

X₃-ISOCONJUGATE OF X₁₁₁₃

X₂₅₈₈ = isogonal conjugate of X₁₈₂₂

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

X₂₅₈₈ (X₃-ISOCONJUGATE OF X₁₁₁₃) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {240, 522}, {11, 1313}

• Related Centers: X₂₅₈₆ (-ISOCONJUGATE OF X₂₅₇₄), X₁ (INCENTER), X₂₄₀ (-LINE CONJUGATE OF X₄₈), X₅₂₂ (ISOGONAL CONJUGATE OF X₁₀₉), X₁₁ (FEUERBACH POINT), X₁₃₁₃ (2nd MOSES INTERSECTION)

Trilinears: \((\sec A)/f(a,b,c) : (\sec B)/f(b,c,a) : (\sec C)/f(c,a,b)\), where f(a,b,c) is as at X₁₁₁₃

Barycentrics: \((\tan A)/f(a,b,c) : (\tan B)/f(b,c,a) : (\tan C)/f(c,a,b)\)

Search Value (6, 9, 13): \(-9.480513160296\)

▸ Incident Central Lines10 lines

{1, 2582}, {10, 2592}, {11, 1313}, {19, 2578}, {65, 2574}, {162, 1822}, {240, 522}, {759, 1114}, {897, 2581}, {1910, 2577}

▸ Functional Relations3 relations

• X₂₅₈₈ = isogonal conjugate of X₁₈₂₂

• X₂₅₈₈ = X₂₅₈₆-Ceva conjugate of X₁

• X₂₅₈₈ = Mimosa transform of X₁₁₁₃

Notes

The following ten points lie on a circle: X_i for i = 11, 36, 65, 80, 108, 759, 1354, 1845, 2588, 2589. (Chris Van Tienhoven, Hyacinthos, January 4, 2011)