X₂₅₇₁

EXSIMILICENTER(ORTHOCENTROIDALCIRCLE, 2nd BROCARD CIRCLE)

X₂₅₇₁ is the exsimilicenter(orthocentroidalcircle, 2nd Brocard circle).

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

X₂₅₇₁ (EXSIMILICENTER(ORTHOCENTROIDALCIRCLE, 2nd BROCARD CIRCLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {2, 3} (Euler line)

• Related Centers: X₂ (CENTROID), X₃ (CIRCUMCENTER), X₄ (ORTHOCENTER)

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = (1 - J/e)\cos A + 4 \cos B \cos C\), J as at X₁₁₁₃, \(e = (1 - 4 \sin^{2}\omega )^{1/2}\)

Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)

Search Value (6, 9, 13): \(-43.659667384834\)

▸ Incident Central Lines1 line

{2, 3}

Notes

As a point on the Euler line, X₂₅₇₁ has Shinagawa coefficients \((-J/e + 1, J/e + 3)\).