X₃₄₃₆

ISOGONAL CONJUGATE OF X₃₄₃₅

X₃₄₃₆ is the isogonal conjugate of X₃₄₃₅.

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

X₃₄₃₆ (ISOGONAL CONJUGATE OF X₃₄₃₅) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {4, 8}, {2, 12}

• Related Centers: X₃₄₃₅ (-VERTEX CONJUGATE OF X₈), X₄ (ORTHOCENTER), X₈ (NAGEL POINT), X₂ (CENTROID), X₁₂ ({X)

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = 1/x(3445)\)

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

Search Value (6, 9, 13): \(7.513868331092\)

▸ Alternate Coordinates1 form

• Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = a^{4} + 2a^{2}bc - 2abc(b + c) - (b^{2} - c^{2})^{2} (E\). Danneels)

▸ Incident Central Lines18 lines

{1, 908}, {2, 12}, {4, 8}, {5, 956}, {10, 46}, {20, 100}, {69, 313}, {78, 515}, {144, 1654}, {145, 497}, {271, 1542}, {315, 668}, {341, 1370}, {405, 495}, {452, 1621}, {498, 993}, {518, 1837}, {519, 1479}

▸ Functional Relations10 relations

• X₃₄₃₆ = reflection of X_i in X_j for these (i,j): (46, 10), (56, 1329), (145, 2098)

• X₃₄₃₆ = isogonal conjugate of X₃₄₃₅

• X₃₄₃₆ = isotomic conjugate of X₈₀₄₈

• X₃₄₃₆ = anticomplement of X₅₆

• X₃₄₃₆ = anticomplementary conjuate of X₁₄₅

• X₃₄₃₆ = X₄₇₈-cross conjugate of X₂

• X₃₄₃₆ = Fuhmann-circle-inverse of X₃₄₃₄

• X₃₄₃₆ = complementary conjugate of complement of X₃₈₂₇₃

• X₃₄₃₆ = homothetic center of anticomplementary triangle and cross-triangle of ABC and outer Johnson triangle

• X₃₄₃₆ = homothetic center of outer Johnson triangle and cross-triangle of ABC and outer Johnson triangle