X₁₃₀₁

COLLINGS TRANSFORM OF X₂₃₅

X₁₃₀₁ = X₅₂₀-cross conjugate of X₄

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

X₁₃₀₁ (COLLINGS TRANSFORM OF X₂₃₅) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {24, 64}, {4, 122}

• Related Centers: X₅₂₀ (ISOGONAL CONJUGATE OF X₁₀₇), X₄ (ORTHOCENTER), X₂₄ (PERSPECTOR OF ABC AND ORTHIC-OF-ORTHIC TRIANGLE), X₆₄ (ISOGONAL CONJUGATE OF X₂₀), X₁₂₂ (-OF-MEDIAL-TRIANGLE)

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

Search Value (6, 9, 13): \(0.440185391326\)

X₁₃₀₁ lies on the circumcircle.

▸ Incident Central Lines7 lines

{4, 122}, {24, 64}, {25, 1073}, {28, 1295}, {98, 459}, {162, 934}, {403, 477}

▸ Functional Relations14 relations

• X₁₃₀₁ = anticomplement of X₃₅₉₆₈

• X₁₃₀₁ = X₅₂₀-cross conjugate of X₄

• X₁₃₀₁ = cevapoint of X_i and X_j for these (i,j): (25, 647), (235, 523)

• X₁₃₀₁ = isogonal conjguate of X₈₀₅₇

• X₁₃₀₁ = trilinear pole of line X₆X₆₄

• X₁₃₀₁ = concurrence of reflections in sides of ABC of line X₄X₆₄

• X₁₃₀₁ = Ψ(X₃, X₆₄)

• X₁₃₀₁ = Ψ(X₄, X₆₄)

• X₁₃₀₁ = Ψ(X₆, X₆₄)

• X₁₃₀₁ = Ψ(X₆₉, X₂₀)

• X₁₃₀₁ = Λ(X₆₅₈₇, X₈₀₅₇) (line X₆₅₈₇X_8057 is the trilinear polar of X₂₀, which is also perspectrix of ABC and half-altitude triangle)

• X₁₃₀₁ = polar-circle-inverse of X₁₂₂

• X₁₃₀₁ = Moses-radical-circle-inverse of X₃₂₆₈₇

• X₁₃₀₁ = X₆₃-isoconjugate of X₆₅₈₇