X₂₆₂₄

SUM OF PU(73)

X₂₆₂₄ = crosssum of X₁ and X₂₆₂₄

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

X₂₆₂₄ (SUM OF PU(73)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {44, 513}, {163, 1983}

• Related Centers: X₄₄ (-LINE CONJUGATE OF X₁), X₅₁₃ (ISOGONAL CONJUGATE OF X₁₀₀), X₁₆₃ (TRILINEAR PRODUCT X₆*X₁₁₀), X₁₉₈₃ (VEGA TRANSFORM OF X₅₂₃)

Trilinears: \(\cot(A - B) + \cot(A - C) : :\)

Search Value (6, 9, 13): \(-15.449693510166\)

▸ Incident Central Lines3 lines

{44, 513}, {163, 1983}, {1109, 2628}

▸ Functional Relations7 relations

• X₂₆₂₄ = isogonal conjugate of X₃₂₆₈₀

• X₂₆₂₄ = crosssum of X₁ and X₂₆₂₄

• X₂₆₂₄ = bicentric sum of PU(73)

• X₂₆₂₄ = crossdifference of every pair of points on line X₁X₅₆₄

• X₂₆₂₄ = polar conjugate of isotomic conjugate of isogonal conjugate of X₃₆₁₂₉

• X₂₆₂₄ = X₆₃-isoconjugate of X₃₆₁₂₉

• X₂₆₂₄ = PU(73)-harmonic conjugate of X₁₁₀₉

Notes

Let J_aJ_bJ_c be the excentral triangle, and let H be the hyperbola {{X₁,X₅,X₃₀,J_a,J_b,J_c}}. Then X₂₆₂₄ is the perspector wrt J_aJ_bJ_c of H. (Randy Hutson, December 26, 2015)

Let H be the rectangular hyperbola passing through X₁, X₅, X₃₀ and the excenters (centered at X₄₇₆); then X₂₆₂₄ is the isogonal conjugate of the perspector of ABC and the tangential triangle, wrt excentral triangle, of H. (Randy Hutson, February 10, 2016)