X₂₉₉₄

CD(X₁₉)

X₂₉₉₄ = pole wrt polar circle of trilinear polar of X₁₀₆₈

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

X₂₉₉₄ (CD(X₁₉)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {8, 90}, {312, 319}

• Related Centers: X₂₁₇₈ (-ISOCONJUGATE OF X₉₀), X₈ (NAGEL POINT), X₉₀ (-CROSS CONJUGATE OF X₁), X₃₁₂ (ISOTOMIC CONJUGATE OF X₅₇), X₃₁₉ (ISOTOMIC CONJUGATE OF X₇₉)

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 P = X₁₉

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

Search Value (6, 9, 13): \(3.304562501415\)

▸ Incident Central Lines8 lines

{2, 914}, {8, 90}, {29, 1069}, {92, 1947}, {281, 1993}, {312, 319}, {333, 2164}, {394, 1146}

▸ Functional Relations8 relations

• X₂₉₉₄ = isogonal conjugate of X₂₁₇₈

• X₂₉₉₄ = cevapoint of X_i and X_j for these (i,j): (521, 1146), (1069, 2164)

• X₂₉₉₄ = isotomic conjugate of X₅₉₀₅

• X₂₉₉₄ = X_i-cross conjugate of X_j for these (i,j): (63, 2), (1479, 7)

• X₂₉₉₄ = cyclocevian conjugate of X₇₂₁₉

• X₂₉₉₄ = pole wrt polar circle of trilinear polar of X₁₀₆₈

• X₂₉₉₄ = X₄₈-isoconjugate (polar conjugate) of X₁₀₆₈

• X₂₉₉₄ = barycentric product of PU(129)