X₁₂₉₄

COLLINGS TRANSFORM OF X₁₂₂

X₁₂₉₄ = cevapoint of X₃ and X₃₀

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

X₁₂₉₄ (COLLINGS TRANSFORM OF X₁₂₂) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {3, 107}, {4, 122}

• Related Centers: X₃ (CIRCUMCENTER), X₁₀₇ (Ψ(SYMMEDIAN POINT, ORTHOCENTER)), X₄ (ORTHOCENTER), X₁₂₂ (-OF-MEDIAL-TRIANGLE)

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

Barycentrics: \(1/(a^{6} (b^{2} + c^{2}) - a^{4} (3 b^{4} - 4 b^{2} c^{2} + 3 c^{4}) + 3 a^{2} (b^{2} - c^{2})^{2} (b^{2} + c^{2}) - (b^{2} - c^{2})^{2} (b^{4} + 4 b^{2} c^{2} + c^{4})) : :\)

Search Value (6, 9, 13): \(13.319367800457\)

X₁₂₉₄ lies on the circumcircle.

▸ Incident Central Lines9 lines

{2, 133}, {3, 107}, {4, 122}, {20, 110}, {22, 1302}, {30, 1304}, {112, 376}, {378, 1289}, {550, 933}

▸ Functional Relations17 relations

• X₁₂₉₄ = reflection of X_i in X_j for these (i,j): (4, 122), (107, 3)

• X₁₂₉₄ = complement of X₃₄₅₄₉

• X₁₂₉₄ = cevapoint of X₃ and X₃₀

• X₁₂₉₄ = X₁₉₃-Hirst inverse of X₂₉₇

• X₁₂₉₄ = isogonal conjugate of X₆₀₀₀

• X₁₂₉₄ = anticomplement of X₁₃₃

• X₁₂₉₄ = Λ(X₇₄, X₁₈₆)

• X₁₂₉₄ = Λ(X₅, X₂₈₈₃)

• X₁₂₉₄ = X₁₃₄-of-hexyl-triangle

• X₁₂₉₄ = eigencenter of circumanticevian triangle of X₄

• X₁₂₉₄ = Cundy-Parry Phi transform of X₁₄₂₄₉

• X₁₂₉₄ = Cundy-Parry Psi transform of X₁₄₃₇₉

• X₁₂₉₄ = Thomson-isogonal conjugate of X₅₂₀

• X₁₂₉₄ = Lucas-isogonal conjugate of X₅₂₀

• X₁₂₉₄ = trilinear pole, wrt Thomson triangle, of line X₆₄X₆₃₁

• X₁₂₉₄ = the point of intersection, other than A, B, and C, of the circumcircle and hyperbola {A, B, C,X₄,X₂₀} (circumconic centered at X₁₂₂)

• X₁₂₉₄ = trilinear pole, wrt circumcevian triangle of X₃₀, of line X₂₂X₄₇₆