X₃₃₅₀

INTERSECTION OF LINES X₃X_2131 AND X₄X_1073

X₃₃₅₀ = X₂-Ceva conjugate of X₃₃₄₄

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

X₃₃₅₀ (INTERSECTION OF LINES X₃X_2131 AND X₄X_1073) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {4, 1073}, {3, 2131}

• Related Centers: X₂ (CENTROID), X₃₃₄₄ (ISOGONAL CONJUGATE OF X₃₃₄₃), X₄ (ORTHOCENTER), X₁₀₇₃ (-CROSS CONJUGATE OF X₃), X₃ (CIRCUMCENTER), X₂₁₃₁ (ISOGONAL CONJUGATE OF X₂₁₃₀)

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = bc[x + y + z - 2yz(y + z - x)/(y^{2} + z^{2} - x^{2})]\), where x : y : \(z = 1/(b^{2} + c^{2} - a^{2}) : 1/(c^{2} + a^{2} - b^{2}) : 1/(a^{2} + b^{2} - c^{2})\) (M. Iliev, 10/27/08)

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

Search Value (6, 9, 13): \(4.108121564009\)

X₃₃₅₀ lies on the Thomson cubic.

▸ Incident Central Lines6 lines

{1, 3352}, {2, 3349}, {3, 2131}, {4, 1073}, {6, 3344}, {57, 3342}

▸ Functional Relations8 relations

• X₃₃₅₀ = isogonal conjugate of X₃₃₄₉

• X₃₃₅₀ = X₂-Ceva conjugate of X₃₃₄₄

• X₃₃₅₀ = X₆-cross conjugate of X₃₃₅₆

• X₃₃₅₀ = perspector of ABC and antipedal triangle of X₂₁₃₁

• X₃₃₅₀ = perspector of pedal and anticevian triangles of X₃₃₅₅

• X₃₃₅₀ = perspector of ABC and medial triangle of pedal triangle of X₂₁₃₀

• X₃₃₅₀ = perspector of circumconic centered at X₃₃₄₄

• X₃₃₅₀ = center of circumconic that is locus of trilinear poles of lines passing through X₃₃₄₄