X₂₅₅₄

1st INTERSECTION(EULER LINE, 2nd BROCARD CIRCLE)

Of the two points of intersection, X₂₅₅₄ is one closer to X₄.

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

X₂₅₅₄ (1st INTERSECTION(EULER LINE, 2nd BROCARD CIRCLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {2555, 3}, {2, 3} (Euler line)

• Related Centers: X₂₅₅₅ (2nd INTERSECTION), X₃ (CIRCUMCENTER), X₂ (CENTROID)

Trilinears: \(f(A,B,C) : f(B,C,A) : f(C,A,B)\), where \(f(A,B,C) = (1 - J/e)\cos A - 2 \cos B \cos C\), J as at X₁₁₁₃.

Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)

Search Value (6, 9, 13): \(1.810717625496\)

▸ Incident Central Lines1 line

{2, 3}

▸ Functional Relations1 relation

• X₂₅₅₄ = reflection of X₂₅₅₅ in X₃

Notes

As a point on the Euler line, X₂₅₅₄ has Shinagawa coefficients \((-J/e + 1, J/e - 3)\).