X₂₅₇₉

X₂-ISOCONJUGATE OF X₁₁₁₄

X₂₅₇₉ = isogonal conjugate of X₂₅₈₁

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

X₂₅₇₉ (X₂-ISOCONJUGATE OF X₁₁₁₄) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {44, 513}, {163, 1823}

• Related Centers: X₂₅₈₁ (-ISOCONJUGATE OF X₂₅₇₅), X₄₄ (-LINE CONJUGATE OF X₁), X₅₁₃ (ISOGONAL CONJUGATE OF X₁₀₀), X₁₆₃ (TRILINEAR PRODUCT X₆*X₁₁₀), X₁₈₂₃ (ISOGONAL CONJUGATE OF X₂₅₈₉)

Trilinears: \(a/f(a,b,c) : b/f(b,c,a) : c/f(c,a,b)\), where f(a,b,c) = X₁₁₁₄

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

Search Value (6, 9, 13): \(-3.520897267135\)

▸ Incident Central Lines9 lines

{19, 2589}, {44, 513}, {48, 2585}, {63, 2583}, {71, 2575}, {163, 1823}, {1113, 2249}, {1821, 2580}, {2159, 2576}

▸ Functional Relations6 relations

• X₂₅₇₉ = isogonal conjugate of X₂₅₈₁

• X₂₅₇₉ = X_i-Ceva conjugate of X_j for these: (i,j): (163,2578), (662,2584), (1823,31), (2577,48), (2581,1), (2583,2585)

• X₂₅₇₉ = cevapoint of X_i and X_j for these {i,j}: {1577, 2580}, {2577, 2587}, {2589, 75}

• X₂₅₇₉ = crosspoint of X_i and X_j for these (i,j): (1, 2581), (19, 2577), (63, 1823), (2583, 2589)

• X₂₅₇₉ = crosssum of X_i and X_j for these (i,j): (1, 2579), (19, 2589), (63, 2583), (1823, 2577)

• X₂₅₇₉ = X₂₅₈₁-aleph conjugate of X₂₅₇₉