X₁₀₇₃

X₆-CROSS CONJUGATE OF X₃

X₁₀₇₃ = X₂₅₃-Ceva conjugate of X₆₄

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

X₁₀₇₃ (X₆-CROSS CONJUGATE OF X₃) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {3, 64}, {9, 223}

• Related Centers: X₆ (SYMMEDIAN POINT), X₃ (CIRCUMCENTER), X₆₄ (ISOGONAL CONJUGATE OF X₂₀), X₉ (MITTENPUNKT), X₂₂₃ (-CEVA CONJUGATE OF X₅₇)

Trilinears: \(f(A,B,C) : f(B,C,A) : f(C,A,B)\), where \(f(A,B,C) = (\cot A)/(\cos A - \cos B \cos C)\)

Barycentrics: \(g(A,B,C) : g(B,C,A) : g(C,A,B)\), where \(g(A,B,C) = (\sin A) f(A,B,C)\)

Search Value (6, 9, 13): \(3.183257130068\)

X₁₀₇₃ lies on the Thomson cubic.

▸ Incident Central Lines8 lines

{1, 3341}, {2, 253}, {3, 64}, {4, 3350}, {6, 3343}, {9, 223}, {57, 3351}, {222, 268}

▸ Functional Relations14 relations

• X₁₀₇₃ = isogonal conjugate of X₁₂₄₉

• X₁₀₇₃ = complement of X₁₄₃₆₁

• X₁₀₇₃ = anticomplement of X₂₀₂₀₇

• X₁₀₇₃ = X₂₅₃-Ceva conjugate of X₆₄

• X₁₀₇₃ = cevapoint of X₆ and X₆₄

• X₁₀₇₃ = X_i-cross conjugate of X_j for these (i,j): (6, 3), (185, 69)

• X₁₀₇₃ = crosssum of X₆ and X₁₀₃₃

• X₁₀₇₃ = isotomic conjugate of X₁₅₄₆₆

• X₁₀₇₃ = perspector of ABC and antipedal triangle of X₁₄₉₈

• X₁₀₇₃ = perspector of pedal and anticevian triangles of X₆₄

• X₁₀₇₃ = perspector of ABC and medial triangle of pedal triangle of X₃₃₄₆

• X₁₀₇₃ = perspector of circumconic centered at X₃₃₄₃

• X₁₀₇₃ = center of circumconic that is locus of trilinear poles of lines passing through X₃₃₄₃

• X₁₀₇₃ = X₂-Ceva conjugate of X₃₃₄₃