X₂₂₈₃

X₂-ISOCONJUGATE OF X₁₀₂₄

X₂₂₈₃ = isogonal conjugate of X₈₈₅

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

X₂₂₈₃ (X₂-ISOCONJUGATE OF X₁₀₂₄) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {1, 3}, {101, 109}

• Related Centers: X₈₈₅ (ISOTOMIC CONJUGATE OF X₈₈₃), X₁ (INCENTER), X₃ (CIRCUMCENTER), X₁₀₁ (Ψ(INCENTER, SYMMEDIAN POINT)), X₁₀₉ (Ψ(INCENTER, CIRCUMCENTER))

Trilinears: \(a/f(a,b,c) : b/f(b,c,a) : c/f(c,a,b)\), where f(a,b,c) is as in X₁₀₂₄

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

Search Value (6, 9, 13): \(-0.241281482157\)

▸ Incident Central Lines7 lines

{1, 3}, {100, 658}, {101, 109}, {108, 1292}, {692, 1813}, {1025, 1026}, {1308, 2222}

▸ Functional Relations7 relations

• X₂₂₈₃ = isogonal conjugate of X₈₈₅

• X₂₂₈₃ = X_i-Ceva conjugate of X_j for these (i,j): (59, 1362), (927, 651), (1025, 2284)

• X₂₂₈₃ = cevapoint of X_i and X_j for these (i,j): (665, 2223), (672, 926)

• X₂₂₈₃ = X_i-cross conjugate of X_j for these (i,j): (665, 241), (926, 672), (1362, 59)

• X₂₂₈₃ = crosspoint of X_i and X_j for these (i,j): (100, 677), (651, 927), (1025, 1026)

• X₂₂₈₃ = crosssum of X_i and X_j for these (i,j): (513, 676), (650, 926)

• X₂₂₈₃ = trilinear pole of line X₆₇₂X₁₃₆₂