X₂₉₉₀

DC(X₁₀₄)

X₂₉₉₀ = X₁₉-isoconjugate of X₉₁₂

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

X₂₉₉₀ (DC(X₁₀₄)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {28, 110}, {278, 651}

• Related Centers: X₂₈ (CEVAPOINT OF X₁₉ AND X₂₅), X₁₁₀ (FOCUS OF KIEPERT PARABOLA), X₂₇₈ (ISOGONAL CONJUGATE OF X₂₁₉), X₆₅₁ (TRILINEAR POLE OF LINE X₁X₃)

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where f(a,b,c) is as given just before X₂₉₇₉, using U = X₁₀₄

Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)

Search Value (6, 9, 13): \(5.123569137976\)

X₂₉₉₀ lies on the MacBeath circumconic.

▸ Incident Central Lines8 lines

{1, 1331}, {2, 1332}, {28, 110}, {57, 1813}, {278, 651}, {394, 1086}, {908, 2006}, {1022, 1797}

▸ Functional Relations7 relations

• X₂₉₉₀ = isogonal conjugate of X₈₆₀₉

• X₂₉₉₀ = isotomic conjugate of isogonal conjugate of X₃₂₆₅₅

• X₂₉₉₀ = isotomic conjugate of polar conjugate of X₉₁₅

• X₂₉₉₀ = X₁₉-isoconjugate of X₉₁₂

• X₂₉₉₀ = cevapoint of X_i and X_j for these (i,j): (1, 2323), (6, 517)

• X₂₉₉₀ = trilinear pole of line X₃X₅₁₃

• X₂₉₉₀ = X_i-cross conjugate of X_j for these (i,j): (654, 100), (2423, 901)