X₂₀₈₄

PK-TRANSFORM OF X₃₁

X₂₀₈₄ = crosspoint of X₆₆₁ and X₇₉₈

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

X₂₀₈₄ (PK-TRANSFORM OF X₃₁) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {514, 661}, {667, 788}

• Related Centers: X₅₁₄ (ISOGONAL CONJUGATE OF X₁₀₁), X₆₆₁ (CROSSDIFFERENCE OF X₁ AND X₂₁), X₆₆₇ (CROSSDIFFERENCE OF X₂ AND X₃₇), X₇₈₈ (ODD (- 3, 0) INFINITY POINT)

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = a^{2}(b^{4} - c^{4})\)

Search Value (6, 9, 13): \(-10.538232294171\)

▸ Incident Central Lines3 lines

{512, 1500}, {514, 661}, {667, 788}

▸ Functional Relations6 relations

• X₂₀₈₄ = isotomic conjugate of X₃₇₂₀₄

• X₂₀₈₄ = X_i-cross conjugate of X_j for these (i,j): (782, 880), (881, 783)

• X₂₀₈₄ = crosspoint of X₆₆₁ and X₇₉₈

• X₂₀₈₄ = crosssum of X_i and X_j for these (i,j): (662, 799), (2084, 2085)

• X₂₀₈₄ = isogonal conjugate of X₄₅₉₃

• X₂₀₈₄ = crossdifference of every pair of points on line X₃₁X₇₅

Notes

Let L be the isogonal conjugate of the isotomic conjugate of the antiorthic axis (i.e., line X₆₆₇X₇₈₈). Let M be the isotomic conjugate of the isogonal conjugate of the antiorthic axis (i.e., line X₅₁₄X₆₆₁). Then X₂₀₈₄ = L∩M. (Randy Hutson, March 21, 2019)