X₁₅₆₄

ORTHOJOIN OF X₅₈₉

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

X₁₅₆₄ (ORTHOJOIN OF X₅₈₉) 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)

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\) (see note above X₁₅₁₂)

Search Value (6, 9, 13): \(-6.879053901710\)

▸ Incident Central Lines1 line

{2, 3}

Notes

As a point on the Euler line, X₁₅₆₄ has Shinagawa coefficients \(([2(E + F)^{2} - (9E + 8F)S+10S^{2}]S, (E + F)^{2}E - 2(5E - F)(E + F)S + 4(7E - 2F)S^{2} - 22S^{3})\).