X₉₃₅

POINT ALCOR

X₉₃₅ = trilinear pole of line X₆X₆₇ (the radical axis of the orthocentroidal circle and Dao-Moses-Telv circle)

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

X₉₃₅ (POINT ALCOR) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {67, 74}, {98, 186}

• Related Centers: X₆₇ (ISOGONAL CONJUGATE OF X₂₃), X₇₄ (ISOGONAL CONJUGATE OF EULER INFINITY POINT), X₉₈ (TARRY POINT), X₁₈₆ (INVERSE-IN-CIRCUMCIRCLE OF X₄)

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = 1/(bw - cv)\),\(u : v : w\) = X₆₇

Barycentrics: \(1/((b^{2} - c^{2}) (b^{2} + c^{2} - a^{2}) (b^{4} + c^{4} - a^{4} - b^{2} c^{2})) : :\)

Search Value (6, 9, 13): \(1.208870298682\)

X₉₃₅ lies on the circumcircle.

▸ Incident Central Lines9 lines

{4, 842}, {67, 74}, {98, 186}, {99, 3267}, {110, 525}, {111, 468}, {112, 523}, {250, 827}, {378, 477}

▸ Functional Relations12 relations

• X₉₃₅ = anticomplement of X₃₈₉₇₁

• X₉₃₅ = X₆₃-isoconjugate of X₂₄₉₂

• X₉₃₅ = trilinear pole of line X₆X₆₇ (the radical axis of the orthocentroidal circle and Dao-Moses-Telv circle)

• X₉₃₅ = concurrence of reflections in sides of ABC of line X₄X₆₇

• X₉₃₅ = polar conjugate of X₉₉₇₉

• X₉₃₅ = Ψ(X₃, X₆₇)

• X₉₃₅ = Ψ(X₄, X₆₇)

• X₉₃₅ = Ψ(X₆, X₆₇)

• X₉₃₅ = Ψ(X₂₃, X₂)

• X₉₃₅ = Λ(trilinear polar of X₂₃)

• X₉₃₅ = reflection of X₁₁₂ in the Euler line

• X₉₃₅ = inverse-in-polar-circle of X₅₀₉₉