X₂₆₉₈

SR(X₉₈, X₉₉)

X₂₆₉₈ = reflection of X₉₈ in the Brocard axis

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

X₂₆₉₈ (SR(X₉₈, X₉₉)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {110, 237}, {107, 419}

• Related Centers: X₂₇₈₂ (ISOGONAL CONJUGATE OF X₂₆₉₈), X₁₁₀ (FOCUS OF KIEPERT PARABOLA), X₂₃₇ (-LINE CONJUGATE OF X₂), X₁₀₇ (Ψ(SYMMEDIAN POINT, ORTHOCENTER)), X₄₁₉ (-HIRST INVERSE OF X₂₅)

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where f(a,b,c) is as given just before X₂₆₇₇ using P = X₉₈, U = X₉₉

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

Search Value (6, 9, 13): \(13.340900855770\)

X₂₆₉₈ lies on the circumcircle.

▸ Incident Central Lines11 lines

{3, 805}, {4, 2679}, {32, 2715}, {98, 512}, {99, 511}, {107, 419}, {110, 237}, {112, 1691}, {182, 691}, {401, 925}, {476, 1316}

▸ Functional Relations10 relations

• X₂₆₉₈ = reflection of X_i in X_j for these (i,j): (4, 2679), (3, 805)

• X₂₆₉₈ = isogonal conjugate of X₂₇₈₂

• X₂₆₉₈ = anticomplement of X₃₃₃₃₀

• X₂₆₉₈ = reflection of X₉₈ in the Brocard axis

• X₂₆₉₈ = Collings transform of X₂₆₇₉

• X₂₆₉₈ = Cundy-Parry Phi transform of X₁₄₂₅₁

• X₂₆₉₈ = Cundy-Parry Psi transform of X₁₄₃₈₂

• X₂₆₉₈ = the point of intersection, other than A, B, and C, of the circumcircle and hyperbola {{A, B, C,X₄,X₃₂}}

• X₂₆₉₈ = inverse-in-circle-{X₁₆₈₇,X₁₆₈₈,PU(1),PU(2)} of X₁₁₂

• X₂₆₉₈ = 3rd-Parry-to-circumsymmedial similarity image of X₂