X₂₃₃₈

X₂-ISOCONJUGATE OF X₁₄₅₆

X₂₃₃₈ = X₆₇₂-cross conjugate of X₉

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

X₂₃₃₈ (X₂-ISOCONJUGATE OF X₁₄₅₆) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {9, 77}, {3, 101}

• Related Centers: X₆₇₂ (CROSSDIFFERENCE OF X₁ AND X₅₁₄), X₉ (MITTENPUNKT), X₇₇ (ISOGONAL CONJUGATE OF X₃₃), X₃ (CIRCUMCENTER), X₁₀₁ (Ψ(INCENTER, SYMMEDIAN POINT))

Trilinears: \(a/f(a,b,c) : b/f(b,c,a) : c/f(c,a,b)\), where f(a,b,c) is as in X₁₄₅₆

Barycentrics: \(a^{2}/f(a,b,c) : b^{2}/f(b,c,a): c^{2}/f(c,a,b)\)

Search Value (6, 9, 13): \(4.515149993194\)

▸ Incident Central Lines8 lines

{1, 1783}, {3, 101}, {9, 77}, {78, 644}, {218, 1433}, {219, 480}, {332, 645}, {677, 2323}

▸ Functional Relations3 relations

• X₂₃₃₈ = cevapoint of X_i and X_j for these (i,j): (6, 2272), (220, 2340)

• X₂₃₃₈ = X₆₇₂-cross conjugate of X₉

• X₂₃₃₈ = crosssum of X_i and X_j for these (i,j): (910, 1456), (1458, 2272)

Notes

X₂₃₃₈ is the perspector of the anticevian triangle of X₁₀₃ and the unary cofactor triangle of the intangents triangle. (Randy Hutson, June 7, 2019)