X₃₈₅₇

X₃₅₂₆com(EULER TRIANGLE)

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

X₃₈₅₇ (X₃₅₂₆com(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)

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

Barycentrics: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = 4a^{4} - 9b^{4} - 9c^{4} + 5a^{2}b^{2} + 5a^{2}c^{2} + 18b^{2}c^{2}\)

Search Value (6, 9, 13): \(-1.226982873383\)

▸ Incident Central Lines1 line

{2, 3}

Notes

As a point on the Euler line, X₃₈₅₇ has Shinagawa coefficients \((5, 13)\)