X₄₄₄

EULER LINE INTERCEPT OF LINE X₁₉X_232

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

X₄₄₄ (EULER LINE INTERCEPT OF LINE X₁₉X_232) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {2, 3} (Euler line), {19, 232}

• Related Centers: X₂ (CENTROID), X₃ (CIRCUMCENTER), X₄ (ORTHOCENTER), X₁₉ (CLAWSON POINT), X₂₃₂ (-CEVA CONJUGATE OF X₁₃₂)

Trilinears: \((v + w)\tan A : (w + u)\tan B : (u + v)\tan C\), where \(u : v : w\) = X₂₅₆; e.g., \(u(a,b,c) = 1/(a^{2} + bc)\)

Barycentrics: \((v + w)(\sin A \tan A) : (w + u)(\sin B \tan B) : (u + v)(\sin C \tan C)\)

Search Value (6, 9, 13): \(-1.132256340988\)

▸ Incident Central Lines2 lines

{2, 3}, {19, 232}

Notes

As a point on the Euler line, X₄₄₄ has Shinagawa coefficients \(([\$a\$(E + F) + \$aS_{A}\$ - abc]F,-(E + F)[\$a\$(E + F) + \$aS_{A}\$ + abc])\).