X₆₃₂

9/10*OG

X₆₃₂ = reflection of X₆₃₁ in X₁₄₀

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

X₆₃₂ (9/10*OG) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {631, 140}, {2, 3} (Euler line)

• Related Centers: X₆₃₁ (3/5*OG), X₁₄₀ (MIDPOINT OF X₃ AND X₅), X₂ (CENTROID), X₃ (CIRCUMCENTER)

Trilinears: \((6S_{B}S_{C} + 7S_{A}a^{2})/a\)

Barycentrics: \(\cot B \cot C - 7 : :\)

Search Value (6, 9, 13): \(3.044668202659\)

▸ Alternate Coordinates1 form

• Trilinears: \(7 \cos A + 6 \cos B \cos C : :\)

▸ Incident Central Lines2 lines

{2, 3}, {141, 575}

▸ Functional Relations2 relations

• X₆₃₂ = reflection of X₆₃₁ in X₁₄₀

• X₆₃₂ = complement of X₁₆₅₆

Notes

As a point on the Euler line, X₆₃₂ has Shinagawa coefficients \((7,-1)\).

X₆₃₂ is the {X₂,X₁₄₀}-harmonic conjugate of X₅.