X₂₆₇₉

RS(X₉₈, X₉₉)

X₂₆₇₉ is the center of the rectangular hyperbola that passes through the points A, B, C, and X₃₂.

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

X₂₆₇₉ (RS(X₉₈, X₉₉)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {4, 2698}

• Related Centers: X₄ (ORTHOCENTER), X₂₆₉₈ (SR(X₉₈, X₉₉))

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = a(b^{2} - c^{2})^{2}(a^{4} - b^{2}c^{2})(b^{4} + c^{4} - a^{2}b^{2} - a^{2}c^{2})\) (M. Iliev, 5/13/07)

Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)

Search Value (6, 9, 13): \(3.832140722422\)

X₂₆₇₉ lies on the nine-point circle, the cevian circle of X₅₁₁.

▸ Incident Central Lines4 lines

{2, 805}, {4, 2698}, {114, 325}, {115, 512}

▸ Functional Relations9 relations

• X₂₆₇₉ = midpoint of X₄ and X₂₆₉₈

• X₂₆₇₉ = complement of X₈₀₅

• X₂₆₇₉ = complementary conjugate of X₈₀₄

• X₂₆₇₉ = X_i-Ceva conjugate of X_j for these (i,j): (2, 2491), (4, 804)

• X₂₆₇₉ = crosspoint of X₅₁₁ and X₅₁₂

• X₂₆₇₉ = crosssum of X₉₈ and X₉₉

• X₂₆₇₉ = perspector of circumconic centered at X₂₄₉₁

• X₂₆₇₉ = center of circumconic that is locus of trilinear poles of lines passing through X₂₄₉₁

• X₂₆₇₉ = crossdifference of every pair of points on line X₂₄₂₁X₂₄₂₂