X₃₁₄₇

X₂₅₄-CEVA CONJUGATE OF X₄

X₃₁₄₇ = X₂₅₄-Ceva conjugate of X₄

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

X₃₁₄₇ (X₂₅₄-CEVA CONJUGATE OF X₄) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {2, 3} (Euler line), {1068, 1940}

• Related Centers: X₂₅₄ (-CROSS CONJUGATE OF X₄), X₄ (ORTHOCENTER), X₂ (CENTROID), X₃ (CIRCUMCENTER), X₁₀₆₈ (-CROSS CONJUGATE OF X₄), X₁₉₄₀ (CROSSSUM OF PU(16))

Trilinears: \(u(-u/x + v/y + w/z) : v(u/x - v/y + w/z) : w(u/x + v/y - w/z)\), where \(x : y : z\) = X₂₅₄ and \(u : v : w\) = X₄

Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\), where \(f(a,b,c) = u(-u/x + v/y + w/z)\)

Search Value (6, 9, 13): \(2.075662213777\)

▸ Incident Central Lines4 lines

{2, 3}, {323, 2904}, {1068, 1940}, {1249, 3003}

▸ Functional Relations2 relations

• X₃₁₄₇ = isogonal conjugate of X₃₈₂₆₀

• X₃₁₄₇ = X₂₅₄-Ceva conjugate of X₄

Notes

As a point on the Euler line, X₃₁₄₇ has Shinagawa coefficients \((4F, -E - 2F)\).