X₄₅₁

X₄-HIRST INVERSE OF X₄₂₄

X₄₅₁ is the X₄-hirst inverse of X₄₂₄.

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

X₄₅₁ (X₄-HIRST INVERSE OF X₄₂₄) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {2, 3} (Euler line), {12, 108}

• Related Centers: X₂ (CENTROID), X₃ (CIRCUMCENTER), X₄ (ORTHOCENTER), X₁₂ ({X), X₁₀₈ (Ψ(CIRCUMCENTER, INCENTER))

Trilinears: \(u \sec A : v \sec B : w \sec C\), where \(u : v : w\) = X₁₉₁

Barycentrics: \(u \tan A : v \tan B : w \tan C\)

Search Value (6, 9, 13): \(3.105963588987\)

▸ Incident Central Lines3 lines

{2, 3}, {12, 108}, {281, 1068}

▸ Functional Relations2 relations

• X₄₅₁ = X₄-Hirst inverse of X₄₂₄

• X₄₅₁ = polar conjugate of X₁₀₂₉

Notes

As a point on the Euler line, X₄₅₁ has Shinagawa coefficients \((2\$a\$F,abc)\).