X₁₅₅₇

ORTHOJOIN OF X₂₆₃

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

X₁₅₅₇ (ORTHOJOIN OF X₂₆₃) 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): \(-5.964707037172\)

▸ Incident Central Lines1 line

{2, 3}

Notes

As a point on the Euler line, X₁₅₅₇ has Shinagawa coefficients \(([(E + F)^{3}F + 2(E + F)^{2}S^{2} + S^{4}] S^{2}, -4(E + F)^{3}F + (E - 11F)(E + F)^{3}S^{2} - (E + 10F)(E + F)S^{4} - 3S^{6})\).