X₂₂₂₆

X₂-ISOCONJUGATE OF X₆₇₈

X₂₂₂₆ = X₆₇₉-Ceva conjugate of X₁₃₁₈

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

X₂₂₂₆ (X₂-ISOCONJUGATE OF X₆₇₈) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {44, 88}, {36, 106}

• Related Centers: X₄₄ (-LINE CONJUGATE OF X₁), X₈₈ (ISOGONAL CONJUGATE OF X₄₄), X₃₆ (INVERSE-IN-CIRCUMCIRCLE OF INCENTER), X₁₀₆ (Λ(INCENTER, CENTROID))

Trilinears: \(a/f(a,b,c) : b/f(b,c,a) : c/f(c,a,b)\), where f(a,b,c) is as in X₆₇₈

Barycentrics: \(a^{2}/f(a,b,c) : b^{2}/f(b,c,a): c^{2}/f(c,a,b)\)

Search Value (6, 9, 13): \(0.034314061513\)

▸ Incident Central Lines2 lines

{36, 106}, {44, 88}

▸ Functional Relations8 relations

• X₂₂₂₆ = isogonal conjugate of X₄₃₇₀

• X₂₂₂₆ = isotomic conjugate of X₃₆₇₉₁

• X₂₂₂₆ = X₆₇₉-Ceva conjugate of X₁₃₁₈

• X₂₂₂₆ = cevapoint of X₆ and X₁₀₆

• X₂₂₂₆ = X_i-cross conjugate of X_j for these (i,j): (6, 106), (649, 901)

• X₂₂₂₆ = X₉₂-isoconjugate of X₂₂₃₇₁

• X₂₂₂₆ = crossdifference of every pair of points on line X₃₂₅₁X₄₅₄₃

• X₂₂₂₆ = trilinear pole of line X₁₀₆X₁₉₆₀ (the tangent to circumcircle at X₁₀₆)