X₁₅₈₀

POINT ALUDRA

X₁₅₈₀ = crossdifference of every pair of points on line X₃₈X₆₆₁

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

X₁₅₈₀ (POINT ALUDRA) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {1, 21}, {41, 43}

• Related Centers: X₁₅₈₁ (ISOGONAL CONJUGATE OF X₁₅₈₀), X₁ (INCENTER), X₂₁ (SCHIFFLER POINT), X₄₁ (-CEVA CONJUGATE OF X₃₁), X₄₃ (-CEVA CONJUGATE OF X₁)

Trilinears: \(a^{4} - b^{2}c^{2} : :\)

Search Value (6, 9, 13): \(-2.227494356736\)

▸ Incident Central Lines11 lines

{1, 21}, {6, 256}, {41, 43}, {75, 560}, {87, 604}, {171, 172}, {238, 1284}, {239, 1281}, {284, 1045}, {661, 830}, {662, 922}

▸ Functional Relations10 relations

• X₁₅₈₀ = isogonal conjugate of X₁₅₈₁

• X₁₅₈₀ = isotomic conjugate of X₁₉₃₄

• X₁₅₈₀ = X_i-Ceva conjugate of X_j for these (i,j): (2, 39043), (1755, 1955), (1910, 1), (1967, 1582)

• X₁₅₈₀ = X₂₂₃₆-cross conjugate of X₁₉₆₆

• X₁₅₈₀ = crosssum of X_i and X_j for these (i,j): (1755, 1964), (1965, 1966)

• X₁₅₈₀ = crossdifference of every pair of points on line X₃₈X₆₆₁

• X₁₅₈₀ = X₉₈-aleph conjugate of X₁₇₅₅

• X₁₅₈₀ = perspector of conic {A, B, C,PU(36)}

• X₁₅₈₀ = trilinear product X₁₇₁*X₂₃₈

• X₁₅₈₀ = perspector of unary cofactor triangles of Gemini triangles 32 and 34