X₁₂₉₈

COLLINGS TRANSFORM OF X₁₃₀

X₁₂₉₈ = anticomplement of X₁₂₉

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

X₁₂₉₈ (COLLINGS TRANSFORM OF X₁₃₀) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {2, 129}, {4, 130}

• Related Centers: X₂ (CENTROID), X₁₂₉ (-OF-ORTHIC-TRIANGLE), X₄ (ORTHOCENTER), X₁₃₀ (-OF-ORTHIC-TRIANGLE)

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\) (see note above X₁₂₈₆)

Search Value (6, 9, 13): \(-0.024037597633\)

X₁₂₉₈ lies on the circumcircle.

▸ Incident Central Lines7 lines

{2, 129}, {3, 1303}, {4, 130}, {51, 107}, {54, 112}, {97, 110}, {184, 933}

▸ Functional Relations7 relations

• X₁₂₉₈ = reflection of X_i in X_j for these (i,j): (4, 130), (1303, 3)

• X₁₂₉₈ = isogonal conjugate of X₃₂₄₂₈

• X₁₂₉₈ = anticomplement of X₁₂₉

• X₁₂₉₈ = X₁₀₇-of-Lucas-triangle (defined at X₉₅)

• X₁₂₉₈ = X₉₉-of-circumorthic-triangle

• X₁₂₉₈ = trilinear pole, wrt Lucas triangle, of line X₂₉₇₉X₃₃₉₇₁

• X₁₂₉₈ = point of intersection, other than A, B, C, of circumcircle and hyperbola {{A, B, C,X₄,X₅₁}} (circumconic centered at X₁₃₀)