X₁₄₉₄

ISOTOMIC CONJUGATE OF X₃₀

X₁₄₉₄ is the isotomic conjugate of X₃₀.

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

X₁₄₉₄ (ISOTOMIC CONJUGATE OF X₃₀) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {648, 2}

• Related Centers: X₆₄₈ (TRILINEAR POLE OF EULER LINE), X₂ (CENTROID)

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = bc/[(b^{2} - c^{2})^{2} + a^{2}(b^{2} + c^{2} - 2a^{2})]\)

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

Search Value (6, 9, 13): \(6.221905711273\)

X₁₄₉₄ lies on the Steiner circumellipse.

▸ Incident Central Lines11 lines

{2, 648}, {30, 340}, {69, 74}, {95, 549}, {190, 306}, {253, 317}, {264, 339}, {287, 524}, {305, 670}, {307, 319}, {325, 892}

▸ Functional Relations12 relations

• X₁₄₉₄ = reflection of X₆₄₈ in X₂

• X₁₄₉₄ = isogonal conjugate of X₁₄₉₅

• X₁₄₉₄ = isotomic conjugate of X₃₀

• X₁₄₉₄ = complement of X₃₉₃₅₈

• X₁₄₉₄ = anticomplement of X₃₁₆₃

• X₁₄₉₄ = cevapoint of X_i and X_j for these (i,j): (2, 30), (3, 323), (298, 299)

• X₁₄₉₄ = X_i-cross conjugate of X_j for these (i,j): (30, 2), (340, 95)

• X₁₄₉₄ = antipode of X₂ in hyperbola {A, B, C,X₂,X₆₉}

• X₁₄₉₄ = trilinear pole of line X₂X₅₂₅

• X₁₄₉₄ = crossdifference of PU(87)

• X₁₄₉₄ = pole wrt polar circle of trilinear polar of x(1990)

• X₁₄₉₄ = X₄₈-isoconjugate (polar conjugate) of X₁₉₉₀