X₃₈₅₄

X₃₅₃₃com(EULER TRIANGLE)

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

X₃₈₅₄ (X₃₅₃₃com(EULER TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {2, 3} (Euler line), {946, 3621}

• Related Centers: X₂ (CENTROID), X₃ (CIRCUMCENTER), X₄ (ORTHOCENTER), X₉₄₆ (MIDPOINT OF X₁ AND X₄), X₃₆₂₁ (H(X₈; M, 2))

Barycentrics: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = 5a^{4} - 11b^{4} - 11c^{4} + 6a^{2}b^{2} + 6a^{2}c^{2} + 22b^{2}c^{2}\)

Search Value (6, 9, 13): \(-1.279331538530\)

▸ Incident Central Lines3 lines

{2, 3}, {946, 3621}, {1699, 3617}

Notes

As a point on the Euler line, X₃₈₅₄ has Shinagawa coefficients \((3, 8)\).