X₃₅₄₀

EULER LINE INTERCEPT OF LINE X₁₀₅₆X_3083

X₃₅₄₀ = inverse-in-orthocentroidal-circle of X₃₅₃₉

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

X₃₅₄₀ (EULER LINE INTERCEPT OF LINE X₁₀₅₆X_3083) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {2, 3} (Euler line), {1056, 3083}

• Related Centers: X₂ (CENTROID), X₃ (CIRCUMCENTER), X₄ (ORTHOCENTER), X₁₀₅₆ (POINT ALCYONE), X₃₀₈₃ (INTERSECTION OF LINES X)

Trilinears: \(f(A,B,C) : f(B,C,A) : f(C,A,B)\), where \(f(A,B,C) = \cos B \cos C - 2 \csc A\)

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

Search Value (6, 9, 13): \(2.938252777356\)

▸ Incident Central Lines3 lines

{2, 3}, {1056, 3083}, {1058, 3084}

▸ Functional Relations1 relation

• X₃₅₄₀ = inverse-in-orthocentroidal-circle of X₃₅₃₉

Notes

As a point on the Euler line, X₃₅₄₀ has Shinagawa coefficients \((2E, -S)\).