X₃₄₃₄

ISOGONAL CONJUGATE OF X₃₄₃₃

X₃₄₃₄ is the isogonal conjugate of X₃₄₃₃.

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

X₃₄₃₄ (ISOGONAL CONJUGATE OF X₃₄₃₃) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {8, 3419}

• Related Centers: X₈ (NAGEL POINT), X₃₄₁₉ (ISOGONAL CONJUGATE OF X₃₄₁₈)

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = 1/x(3433)\)

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

Search Value (6, 9, 13): \(2.617167545192\)

▸ Alternate Coordinates1 form

• Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = a^{3} - a^{2}b - a^{2}c + ab^{2} + ac^{2} - (b + c)(b - c)^{2} (E\). Danneels)

▸ Incident Central Lines22 lines

{1, 224}, {2, 11}, {4, 8}, {10, 1479}, {20, 2894}, {30, 956}, {63, 516}, {69, 674}, {75, 1370}, {78, 946}, {145, 388}, {152, 2807}, {200, 908}, {226, 2900}, {443, 1058}, {474, 496}, {518, 1836}, {519, 1478}, {595, 1714}, {614, 1738}, {1004, 1617}, {1484, 2932}

▸ Functional Relations10 relations

• X₃₄₃₄ = midpoint of X₈ and X₃₄₁₉

• X₃₄₃₄ = reflection of X_i in X_j for these (i,j): (8, 3419), (20, 3428), (55, 2885), (145, 2099)

• X₃₄₃₄ = isogonal conjugate of X₃₄₃₃

• X₃₄₃₄ = inverse-in-Fuhmann circle of X₃₄₃₆

• X₃₄₃₄ = anticomplement of X₅₅

• X₃₄₃₄ = anticomplementary conjuate of X₁₄₄

• X₃₄₃₄ = complementary conjugate of complement of X₃₈₂₆₉

• X₃₄₃₄ = inner-Conway-isogonal conjugate of X₃₄₇₈₄

• X₃₄₃₄ = homothetic center of anticomplementary triangle and cross-triangle of ABC and inner Johnson triangle

• X₃₄₃₄ = homothetic center of inner Johnson triangle and cross-triangle of ABC and inner Johnson triangle