X₁₀₃₄

X₄-CROSS CONJUGATE OF X₈

X₁₀₃₄ = isogonal conjugate of X₁₀₃₅

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

X₁₀₃₄ (X₄-CROSS CONJUGATE OF X₈) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {20, 78}, {2, 271}

• Related Centers: X₄ (ORTHOCENTER), X₈ (NAGEL POINT), X₂₀ (DE LONGCHAMPS POINT), X₇₈ (ISOGONAL CONJUGATE OF X₃₄), X₂ (CENTROID), X₂₇₁ (ISOGONAL CONJUGATE OF X₂₀₈)

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = 1/[a(w^{2}u^{2} + u^{2}v^{2} - v^{2}w^{2}) + 2uvw(au + bv + cw) \cos A]\), where \(u : v : w\) = X₃₂₉

Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = af(a,b,c)\)

Search Value (6, 9, 13): \(5.420104051938\)

X₁₀₃₄ lies on the Lucas cubic.

▸ Incident Central Lines2 lines

{2, 271}, {20, 78}

▸ Functional Relations8 relations

• X₁₀₃₄ = perpsector of triangle ABC and the pedal triangle of X₃₃₄₅

• X₁₀₃₄ = isogonal conjugate of X₁₀₃₅

• X₁₀₃₄ = isotomic conjugate of X₅₉₃₂

• X₁₀₃₄ = trilinear pole of line X₈₀₅₈X_14331

• X₁₀₃₄ = anticomplement of X₃₃₄₂

• X₁₀₃₄ = anticomplementary conjugate of X₃₄₁₆₂

• X₁₀₃₄ = X_i-cross conjugate of X_j for these (i,j): (4, 8), (282, 2)

• X₁₀₃₄ = cyclocevian conjugate of X₃₂₉