X₃₃₄₂

ISOGONAL CONJUGATE OF X₃₃₄₁

X₃₃₄₂ is the isogonal conjugate of X₃₃₄₁.

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

X₃₃₄₂ (ISOGONAL CONJUGATE OF X₃₃₄₁) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {3, 223}, {2, 271}

• Related Centers: X₃₃₄₁ (-CEVA CONJUGATE OF X₂₈₂), X₃ (CIRCUMCENTER), X₂₂₃ (-CEVA CONJUGATE OF X₅₇), X₂ (CENTROID), X₂₇₁ (ISOGONAL CONJUGATE OF X₂₀₈)

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = 1/(x(-ax + by + cz))\), where \(x : y : z\) = X₂₈₂

Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)

Search Value (6, 9, 13): \(2.244041257448\)

X₃₃₄₂ lies on the Thomson cubic.

▸ Incident Central Lines6 lines

{1, 3343}, {2, 271}, {3, 223}, {6, 3351}, {9, 1249}, {57, 3350}

▸ Functional Relations9 relations

• X₃₃₄₂ = isogonal conjugate of X₃₃₄₁

• X₃₃₄₂ = complement of X₃₄₁₆₂

• X₃₃₄₂ = X_i-Ceva conjugate of X_j for these (i,j): (2, 3351), (1034, 3345)

• X₃₃₄₂ = X_i-cross conjugate of X_j for these (i,j): (6, 223), (208, 40)

• X₃₃₄₂ = perspector of ABC and antipedal triangle of X₃₁₈₂

• X₃₃₄₂ = perspector of pedal and anticevian triangles of X₃₃₄₅

• X₃₃₄₂ = perspector of ABC and medial triangle of pedal triangle of X₃₃₄₇

• X₃₃₄₂ = perspector of circumconic centered at X₃₃₅₁

• X₃₃₄₂ = center of circumconic that is locus of trilinear poles of lines passing through X₃₃₅₁