X₈₂₂

CROSSDIFFERENCE OF X₁ AND X₂₉

X₈₂₂ = X₁₆₃-Ceva conjugate of X₄₈

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

X₈₂₂ (CROSSDIFFERENCE OF X₁ AND X₂₉) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {44, 513}

• Related Centers: X₁₆₃ (TRILINEAR PRODUCT X₆*X₁₁₀), X₄₈ (CROSSPOINT OF X₁ AND X₆₃), X₄₄ (-LINE CONJUGATE OF X₁), X₅₁₃ (ISOGONAL CONJUGATE OF X₁₀₀)

Trilinears: \(\sec^{2} B - \sec^{2} C : :\)

Barycentrics: \(\sin A (\sec^{2} B - \sec^{2} C) : :\)

Search Value (6, 9, 13): \(-19.452478177209\)

▸ Alternate Coordinates4 forms

• Trilinears: \(\csc B/2 - \csc C/2 : :\)

• Trilinears: \(\csc 2B - \csc 2C : :\)

• Trilinears: \(\sin 2A (\tan B - \tan C) : :\)

• Trilinears: \(a^{2}(b^{2} - c^{2})(b^{2} + c^{2} - a^{2})^{2} : :\)

▸ Incident Central Lines1 line

{44, 513}

▸ Functional Relations13 relations

• X₈₂₂ = isogonal conjugate of X₈₂₃

• X₈₂₂ = X₁₆₃-Ceva conjugate of X₄₈

• X₈₂₂ = crosspoint of X₄₈ and X₁₆₃

• X₈₂₂ = crosssum of X_i and X_j for these (i,j): (1, 822), (29, 1021), (661, 774)

• X₈₂₂ = crossdifference of every pair of points on line X₁X₂₉

• X₈₂₂ = perspector, wrt excentral triangle, of bianticevian conic of X₁ and X₄

• X₈₂₂ = X₉₂-isoconjugate of X₁₆₂

• X₈₂₂ = bicentric difference of PU(83)

• X₈₂₂ = polar conjugate of isotomic conjugate of isogonal conjugate of X₃₆₁₂₆

• X₈₂₂ = PU(83)-harmonic conjugate of X₂₆₅₈

• X₈₂₂ = X₆₃-isoconjugate of X₃₆₁₂₆

• X₈₂₂ = X₂-Ceva conjugate of X₃₈₉₈₅

• X₈₂₂ = perspector of hyperbola {A, B, C,X₁,X₄₈}}