X₃₁₃₃

X₂₄-CEVA CONJUGATE OF X₅₂

X₃₁₃₃ = X₂₄-Ceva conjugate of X₅₂

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

X₃₁₃₃ (X₂₄-CEVA CONJUGATE OF X₅₂) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {2, 3} (Euler line), {571, 1147}

• Related Centers: X₂₄ (PERSPECTOR OF ABC AND ORTHIC-OF-ORTHIC TRIANGLE), X₅₂ (ORTHOCENTER OF ORTHIC TRIANGLE), X₂ (CENTROID), X₃ (CIRCUMCENTER), X₅₇₁ (ORTHOHARMONIC OF X₅₂), X₁₁₄₇ (ISOGONAL CONJUGATE OF X₈₄₇)

Trilinears: \(u(-u/x + v/y + w/z) : v(u/x - v/y + w/z) : w(u/x + v/y - w/z)\), where \(x : y : z\) = X₂₄ and \(u : v : w\) = X₅₂

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): \(0.800861713797\)

▸ Incident Central Lines2 lines

{2, 3}, {571, 1147}

▸ Functional Relations1 relation

• X₃₁₃₃ = X₂₄-Ceva conjugate of X₅₂

Notes

As a point on the Euler line, X₃₁₃₃ has Shinagawa coefficients \(((E + 2F)(E - 2F) - 4S^{2},(E + 2F)^{2} + 4S^{2})\).