X₄₀₈

EULER LINE INTERCEPT OF LINE X₇₃X_228

X₄₀₈ = crosssum of X₂₉ and X₄₁₂

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

X₄₀₈ (EULER LINE INTERCEPT OF LINE X₇₃X_228) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {2, 3} (Euler line), {73, 228}

• Related Centers: X₂ (CENTROID), X₃ (CIRCUMCENTER), X₄ (ORTHOCENTER), X₇₃ (CROSSPOINT OF INCENTER AND CIRCUMCENTER), X₂₂₈ (-CEVA CONJUGATE OF X₇₁)

Trilinears: \((v + w)\cos A : (w + u)\cos B : (u + v)\cos C\), where \(u : v : w\) = X₂₉; e.g., \(u = u(A,B,C) = (\sec A)/(\cos B + \cos C)\)

Barycentrics: \((v + w)\sin 2A : (w + u)\sin 2B : (u + v)\sin 2C\)

Search Value (6, 9, 13): \(-5.051954769468\)

▸ Incident Central Lines2 lines

{2, 3}, {73, 228}

▸ Functional Relations1 relation

• X₄₀₈ = crosssum of X₂₉ and X₄₁₂

Notes

As a point on the Euler line, X₄₀₈ has Shinagawa coefficients \(((\$bcS_{B}S_{C}\$)^{2}, -(\$bcS_{B}S_{C}\$)^{2} + EFS^{4})\).