X₃₈₆₁

X₅₄₆com(EULER TRIANGLE)

X₃₈₆₁ = {X₄,X₅}-harmonic conjugate of X₃₈₅₃

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

X₃₈₆₁ (X₅₄₆com(EULER TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {4, 5} (Euler line)

• Related Centers: X₃₈₅₃ (com(EULER TRIANGLE)), X₄ (ORTHOCENTER), X₅ (NINE-POINT CENTER)

Barycentrics: \(6a^{4} - 7b^{4} - 7c^{4} + a^{2}b^{2} + a^{2}c^{2} + 14b^{2}c^{2} : :\)

Search Value (6, 9, 13): \(-4.119246622786\)

▸ Linear Combinations1 combination

• X₃₈₆₁ = \(3\) X₄ + X₅

▸ Incident Central Lines1 line

{2, 3}

▸ Functional Relations1 relation

• X₃₈₆₁ = {X₄,X₅}-harmonic conjugate of X₃₈₅₃

Notes

As a point on the Euler line, X₃₈₆₁ has Shinagawa coefficients \((1, 13)\).