X₆₄₂

COMPLEMENT OF X₄₈₆

X₆₄₂ is the complement of X₄₈₆.

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

X₆₄₂ (COMPLEMENT OF X₄₈₆) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {486, 487}

• Related Centers: X₄₈₆ (INNER VECTEN POINT), X₄₈₇ (ANTICOMPLEMENT OF X₄₈₆)

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = [2S_{B}S_{C} + 3S_{A}a^{2} - 2(b^{2} + c^{2}) \operatorname{area}]/a\)

Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = af(a,b,c)\)

Search Value (6, 9, 13): \(3.016792837794\)

▸ Incident Central Lines4 lines

{2, 371}, {3, 640}, {140, 141}, {372, 491}

▸ Functional Relations10 relations

• X₆₄₂ = midpoint of X₄₈₆ and X₄₈₇

• X₆₄₂ = complement of X₄₈₆

• X₆₄₂ = complementary conjugate of X₆₄₀

• X₆₄₂ = crosspoint of X₂ and X₄₉₁

• X₆₄₂ = X₃-of-inner-Vecten-triangle

• X₆₄₂ = inner-Vecten-isogonal conjugate of X₄₈₆

• X₆₄₂ = perspector of circumconic centered at X₆₁₅

• X₆₄₂ = center of circumconic that is locus of trilinear poles of lines passing through X₆₁₅

• X₆₄₂ = X₂-Ceva conjugate of X₆₁₅

• X₆₄₂ = perspector of medial triangle and outer Vecten of inner Vecten triangle (note: the medial triangle is the inner Vecten of inner Vecten triangle.)

Notes

Erect squares inwards on the sides of triangle ABC; the circumcenter of the centers of the squares is X₆₄₂. (Peter Moses, 7/16,2003)