X₁₃₃₄

POINT ALYA

X₁₃₃₄ = crosssum of X_i and X_j for (i,j) = (7,57), (81,1014)

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

X₁₃₃₄ (POINT ALYA) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {8, 9}, {41, 55}

• Related Centers: X₁₄₃₄ (-BETH CONJUGATE OF X₂₇₄), X₈ (NAGEL POINT), X₉ (MITTENPUNKT), X₄₁ (-CEVA CONJUGATE OF X₃₁), X₅₅ (INSIMILICENTER)

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = a(b + c)(b + c - a)\)

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

Search Value (6, 9, 13): \(3.016964988991\)

▸ Incident Central Lines13 lines

{1, 672}, {3, 1055}, {8, 9}, {10, 1018}, {21, 644}, {32, 902}, {35, 101}, {37, 65}, {39, 1201}, {41, 55}, {42, 213}, {607, 1253}, {756, 862}

▸ Functional Relations8 relations

• X₁₃₃₄ = isogonal conjugate of X₁₄₃₄

• X₁₃₃₄ = complement of X₂₀₂₄₄

• X₁₃₃₄ = anticomplement of X₁₇₀₅₀

• X₁₃₃₄ = X_i-Ceva conjugate of X_j for these (i,j): (9, 210), (37, 42), (644, 663)

• X₁₃₃₄ = crosspoint of X_i and X_j for these (i,j): (9, 55), (37, 210)

• X₁₃₃₄ = crosssum of X_i and X_j for (i,j) = (7,57), (81,1014)

• X₁₃₃₄ = crossdifference of every pair of points on line X₁₄₄₃X₁₄₄₇

• X₁₃₃₄ = trilinear pole of line X₁₄₄₃X₁₄₄₇