X₃₂₄₈

CROSSSUM OF X₁ AND X₁₉₀

X₃₂₄₈ = crossdifference of every pair of points on the line X₁₉₀X₆₄₆

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

X₃₂₄₈ (CROSSSUM OF X₁ AND X₁₉₀) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {75, 87}, {1, 190}

• Related Centers: X₇₅ (ISOTOMIC CONJUGATE OF INCENTER), X₈₇ (-CROSS CONJUGATE OF X₁), X₁ (INCENTER), X₁₉₀ (YFF PARABOLIC POINT)

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

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

Search Value (6, 9, 13): \(0.462447763198\)

▸ Incident Central Lines17 lines

{1, 190}, {6, 292}, {31, 692}, {42, 678}, {75, 87}, {86, 2665}, {239, 2234}, {244, 659}, {341, 979}, {560, 604}, {662, 741}, {757, 1178}, {798, 1084}, {890, 1977}, {922, 2210}, {1015, 1960}, {1100, 2309}

▸ Functional Relations7 relations

• X₃₂₄₈ = X_i-Ceva conjugate of X_j for these (i,j): (1, 649), (6, 798), (31, 667), (87, 513), (604, 1919), (649, 3249), (873, 1019), (979, 650), (2297, 2484), (2665, 659)

• X₃₂₄₈ = isogonal conjugate of X₇₀₃₅

• X₃₂₄₈ = X_i-cross conjugate of X_j for these (i,j): (3121, 1015), (3249, 649)

• X₃₂₄₈ = crosspoint of X_i and X_j for these (i,j): (1, 649), (31, 667), (873, 1019), (1015, 1357)

• X₃₂₄₈ = crosssum of X_i and X_j for these (i,j): (1, 190), (75, 668), (341, 646), (872, 1018)

• X₃₂₄₈ = crossdifference of every pair of points on the line X₁₉₀X₆₄₆

• X₃₂₄₈ = trilinear pole wrt incentral triangle of Nagel line