X₃₂₇₀

X₁-CEVA CONJUGATE OF X₆₄₇

X₃₂₇₀ = crossdifference of every pair of points of the line X₆₅₁X₆₅₃

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

X₃₂₇₀ (X₁-CEVA CONJUGATE OF X₆₄₇) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {33, 51}, {11, 125}

• Related Centers: X₁ (INCENTER), X₆₄₇ (CROSSDIFFERENCE OF X₂ AND X₃), X₃₃ (PERSPECTOR OF THE ORTHIC AND INTANGENTS TRIANGLES), X₅₁ (CENTROID OF ORTHIC TRIANGLE), X₁₁ (FEUERBACH POINT), X₁₂₅ (CENTER OF JERABEK HYPERBOLA)

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = a(b - c)^{2}(b + c - a)^{2}(b^{2} + c^{2} - a^{2})\)

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

Search Value (6, 9, 13): \(3.093833480336\)

X₃₂₇₀ lies on the orthic inconic.

▸ Incident Central Lines19 lines

{1, 185}, {3, 1813}, {11, 125}, {25, 2192}, {33, 51}, {55, 184}, {56, 1204}, {64, 1398}, {103, 1461}, {217, 1500}, {497, 1899}, {511, 3100}, {651, 2808}, {926, 2170}, {1069, 1092}, {1409, 2293}, {1827, 2262}, {2637, 2638}, {2876, 3056}

▸ Functional Relations9 relations

• X₃₂₇₀ = X_i-Ceva conjugate of X_j for these (i,j): (1, 647), (3, 652), (4, 650), (6, 657), (64, 649), (74, 654), (2192, 663)

• X₃₂₇₀ = crosspoint of X_i and X_j for these (i,j): (1, 1021), (3, 652), (4, 650), (6, 1459), (1146, 2968)

• X₃₂₇₀ = crosssum of X_i and X_j for these (i,j): (1, 1020), (2, 1897), (3, 651), (4, 653), (7, 934), (100, 329), (108, 278)

• X₃₂₇₀ = crossdifference of every pair of points of the line X₆₅₁X₆₅₃

• X₃₂₇₀ = orthic-isogonal conjugate of X₆₅₀

• X₃₂₇₀ = perspector of orthic triangle and tangential triangle of Feuerbach hyperbola

• X₃₂₇₀ = X₆₃-isoconjugate of X₂₃₉₈₄

• X₃₂₇₀ = X₉₂-isoconjugate of X₁₂₆₂

• X₃₂₇₀ = polar conjugate of isotomic conjugate of X₃₅₀₇₂