X₃₁₁₉

DANNEELS PERSPECTOR FOR X₉

X₃₁₁₉ = X₃₀₂₂-cross conjugate of X₂₃₁₀

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

X₃₁₁₉ (DANNEELS PERSPECTOR FOR X₉) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {9, 100}, {125, 661}

• Related Centers: X₉ (MITTENPUNKT), X₁₀₀ (ANTICOMPLEMENT OF FEUERBACH POINT), X₁₂₅ (CENTER OF JERABEK HYPERBOLA), X₆₆₁ (CROSSDIFFERENCE OF X₁ AND X₂₁)

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = (b - c)^{2}(b + c - a)^{3}\)

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

Search Value (6, 9, 13): \(3.713970196230\)

▸ Incident Central Lines6 lines

{9, 100}, {11, 1146}, {125, 661}, {281, 2171}, {282, 604}, {1200, 1864}

▸ Functional Relations6 relations

• X₃₁₁₉ = complement of X₃₅₃₁₂

• X₃₁₁₉ = X_i-Ceva conjugate of X_j for these (i,j): (85, 522), (282, 663), (1146, 2310)

• X₃₁₁₉ = X₃₀₂₂-cross conjugate of X₂₃₁₀

• X₃₁₁₉ = crosspoint of X_i and X_j for these (i,j): (33, 650), (85, 522), (514, 3062)

• X₃₁₁₉ = crosssum of X_i and X_j for these (i,j): (41, 109), (57, 934), (77, 651), (101, 165), (269, 1461)

• X₃₁₁₉ = crossdifference of every pair of points on the line X₁₀₉X₉₃₄