X₃₂₇₁

CROSSSUM OF X₂ AND X₁₀₀

X₃₂₇₁ = crossdifference of every pair of points of the line X₁₉₀X₆₄₄

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

X₃₂₇₁ (CROSSSUM OF X₂ AND X₁₀₀) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {31, 51}, {11, 124}

• Related Centers: X₃₁ (2nd POWER POINT), X₅₁ (CENTROID OF ORTHIC TRIANGLE), X₁₁ (FEUERBACH POINT), X₁₂₄ (-OF-MEDIAL-TRIANGLE)

Trilinears: \(a(b - c)^{2}(b + c - a) : :\)

Search Value (6, 9, 13): \(1.399414575628\)

▸ Alternate Coordinates3 forms

• Trilinears: \(a^{2} (1 - \cos(B - C)) : :\)

• Trilinears: \(a^{2} \sin^{2}(B/2 - C/2) : :\)

• Trilinears: \(a^{2} \csc^{2}(B/2 - C/2) : :\)

X₃₂₇₁ lies on the Mandart inellipse.

▸ Incident Central Lines35 lines

{1, 2810}, {6, 692}, {8, 646}, {9, 3056}, {11, 124}, {21, 1682}, {25, 1397}, {31, 51}, {44, 674}, {55, 2316}, {56, 1461}, {65, 2835}, {100, 3030}, {105, 651}, {215, 2194}, {238, 511}, {244, 1357}, {373, 750}, {389, 3073}, {512, 2643}, {513, 1086}, {614, 1401}, {926, 2170}, {1015, 1960}, {1083, 1332}, {1361, 1411}, {1365, 2969}, {1428, 3220}, {1843, 2212}, {1977, 3124}, {2092, 2309}, {2161, 2875}, {2183, 2223}, {2293, 2347}, {3125, 4560}

▸ Functional Relations7 relations

• X₃₂₇₁ = isogonal conjugate of X₄₉₉₈

• X₃₂₇₁ = X_i-Ceva conjugate of X_j for these (i,j): (6, 3063), (8, 650), (25, 667), (31, 512), (42, 2488), (55, 663), (56, 649), (105, 665), (244, 1015), (263, 788), (1411, 3310), (2218, 647)

• X₃₂₇₁ = crosspoint of X_i and X_j for these (i,j): (6, 513), (55, 663), (56, 651), (244, 2170)

• X₃₂₇₁ = crosssum of X_i and X_j for these (i,j): (2, 100), (7, 664), (8, 190), (56, 651), (480, 644), (1259, 1332)

• X₃₂₇₁ = crossdifference of every pair of points of the line X₁₉₀X₆₄₄

• X₃₂₇₁ = X₅₉-isoconjugate of X₇₅

• X₃₂₇₁ = trilinear square of X₆₇₂₉