X₂₁₈₈

X₂-ISOCONJUGATE OF X₁₉₆

X₂₁₈₈ = isogonal conjugate of X₃₄₂

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

X₂₁₈₈ (X₂-ISOCONJUGATE OF X₁₉₆) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {48, 55}, {282, 284}

• Related Centers: X₃₄₂ (ISOTOMIC CONJUGATE OF X₂₇₁), X₄₈ (CROSSPOINT OF X₁ AND X₆₃), X₅₅ (INSIMILICENTER), X₂₈₂ (-CROSS CONJUGATE OF X₉), X₂₈₄ (-CROSS CONJUGATE OF X₂₁)

Trilinears: \(a/f(a,b,c) : b/f(b,c,a) : c/f(c,a,b)\), where f(a,b,c) is as in X₁₉₆

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

Search Value (6, 9, 13): \(2.765413339863\)

▸ Incident Central Lines12 lines

{1, 1767}, {3, 1433}, {48, 55}, {57, 972}, {73, 972}, {73, 939}, {84, 943}, {212, 577}, {268, 1260}, {271, 1792}, {282, 284}, {1903, 2268}

▸ Functional Relations5 relations

• X₂₁₈₈ = isogonal conjugate of X₃₄₂

• X₂₁₈₈ = X_i-cross conjugate of X_j for these (i,j): (41, 48), (184, 212)

• X₂₁₈₈ = crosspoint of X_i and X_j for these (i,j): (268, 1433), (271, 282)

• X₂₁₈₈ = crosssum of X_i and X_j for these (i,j): (1, 1767), (208, 223)

• X₂₁₈₈ = X₉₂-isoconjugate of X₂₂₃