X₂₈₂

X₆-CROSS CONJUGATE OF X₉

X₂₈₂ = isogonal conjugate of X₂₂₃

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

X₂₈₂ (X₆-CROSS CONJUGATE OF X₉) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {3, 9}, {2, 77}

• Related Centers: X₆ (SYMMEDIAN POINT), X₉ (MITTENPUNKT), X₃ (CIRCUMCENTER), X₂ (CENTROID), X₇₇ (ISOGONAL CONJUGATE OF X₃₃)

Trilinears: \((\cot A/2)/(-1 - \cos A + \cos B + \cos C) : :\)

Search Value (6, 9, 13): \(4.538313100759\)

X₂₈₂ lies on the Thomson cubic.

▸ Incident Central Lines12 lines

{1, 281}, {2, 77}, {3, 9}, {4, 3351}, {6, 3341}, {19, 102}, {48, 947}, {57, 3343}, {78, 280}, {200, 219}, {271, 283}, {380, 1036}

▸ Functional Relations15 relations

• X₂₈₂ = isogonal conjugate of X₂₂₃

• X₂₈₂ = isotomic conjugate of isogonal conjugate of X₇₁₁₈

• X₂₈₂ = complement of X₅₉₃₂

• X₂₈₂ = anticomplement of X₂₀₂₀₆

• X₂₈₂ = X₁₈₉-Ceva conjugate of X₈₄

• X₂₈₂ = X_i-cross conjugate of X_j for these (i,j): (6, 9), (33, 1)

• X₂₈₂ = crosspoint of X₁₈₉ and X₂₈₀

• X₂₈₂ = crosssum of X_i and X_j for these (i,j): (6, 1035), (198, 221)

• X₂₈₂ = perspector of ABC and antipedal triangle of X₁₄₉₀

• X₂₈₂ = perspector of pedal and anticevian triangles of X₈₄

• X₂₈₂ = perspector of ABC and medial triangle of pedal triangle of X₃₃₄₅

• X₂₈₂ = perspector of circumconic centered at X₃₃₄₁

• X₂₈₂ = center of circumconic that is locus of trilinear poles of lines passing through X₃₃₄₁

• X₂₈₂ = X₂-Ceva conjugate of X₃₃₄₁

• X₂₈₂ = polar conjugate of X₃₄₂