X₂₃₄₉

X₂-ISOCONJUGATE OF X₁₄₉₅

X₂₃₄₉ = isogonal conjugate of X₂₁₇₃

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

X₂₃₄₉ (X₂-ISOCONJUGATE OF X₁₄₉₅) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {72, 74}, {1, 162}

• Related Centers: X₂₁₇₃ (-ISOCONJUGATE OF X₇₄), X₇₂ (ISOGONAL CONJUGATE OF X₂₈), X₇₄ (ISOGONAL CONJUGATE OF EULER INFINITY POINT), X₁ (INCENTER), X₁₆₂ (CEVAPOINT OF X₁₀₈ AND X₁₀₉)

Trilinears: \(a/f(a,b,c) : b/f(b,c,a) : c/f(c,a,b)\), where f(a,b,c) is as in X₁₄₉₅

Barycentrics: \(1/(\cos A - 2 \cos B \cos C) : :\)

Search Value (6, 9, 13): \(6.952296728786\)

▸ Alternate Coordinates1 form

• Barycentrics: \(1/(3 \cos A - 2 \sin B \sin C) : :\)

▸ Incident Central Lines10 lines

{1, 162}, {63, 662}, {72, 74}, {92, 823}, {190, 306}, {226, 653}, {293, 896}, {304, 799}, {651, 1214}, {1748, 2184}

▸ Functional Relations8 relations

• X₂₃₄₉ = isogonal conjugate of X₂₁₇₃

• X₂₃₄₉ = isotomic conjugate of X₁₄₂₀₆

• X₂₃₄₉ = polar conjugate of X₁₇₈₄

• X₂₃₄₉ = trilinear pole of line X₁X₆₅₆

• X₂₃₄₉ = X₆-isoconjugate of X₃₀

• X₂₃₄₉ = cevapoint of X_i and X_j for these (i,j): (1, 2173), (9, 758), (2631, 2632)

• X₂₃₄₉ = X_i-cross conjugate of X_j for these (i,j): (1725, 75), (2173, 1), (2631, 162)

• X₂₃₄₉ = X_i-aleph conjugate of X_j for these (i,j): (74, 1740), (1494, 63), (2349, 1)