X₂₁₇₃

X₂-ISOCONJUGATE OF X₇₄

X₂₁₇₃ = crossdifference of every pair of points on line X₁X₆₅₆

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

X₂₁₇₃ (X₂-ISOCONJUGATE OF X₇₄) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {1, 19}, {45, 198}

• Related Centers: X₂₃₄₉ (-ISOCONJUGATE OF X₁₄₉₅), X₁ (INCENTER), X₁₉ (CLAWSON POINT), X₄₅ (-BETH CONJUGATE OF X₁), X₁₉₈ (-CEVA CONJUGATE OF X₆)

Trilinears: \(a/f(a,b,c) : b/f(b,c,a) : c/f(c,a,b)\), where f(a,b,c) is as in X₇₄

Search Value (6, 9, 13): \(-3.645102576970\)

▸ Alternate Coordinates4 forms

• Trilinears: \(a(\cos A - 2 \cos B \cos C) : :\)

• Trilinears: \(a(3 \cos A - 2 \sin B \sin C) : :\)

• Trilinears: \(3 \sin 2A - 4 \sin A \sin B \sin C : :\)

• Trilinears: \(2a^{4} - b^{4} - c^{4} - a^{2}b^{2} - a^{2}c^{2} + 2b^{2}c^{2} : :\)

▸ Incident Central Lines20 lines

{1, 19}, {6, 1406}, {36, 1731}, {44, 513}, {45, 198}, {169, 2267}, {662, 1959}, {897, 1910}, {1405, 1454}, {1725, 2159}, {1760, 1958}, {1761, 2287}, {1762, 1817}, {1820, 2155}, {2151, 2153}, {2152, 2154}, {2171, 2174}, {2260, 2264}, {2261, 2270}, {2262, 2317}

▸ Functional Relations9 relations

• X₂₁₇₃ = isogonal conjugate of X₂₃₄₉

• X₂₁₇₃ = X_i-Ceva conjugate of X_j for these (i,j): (2341, 6), (2349, 1)

• X₂₁₇₃ = crosspoint of X_i and X_j for these (i,j): (1, 2349), (57, 759), (92, 2166), (2153, 2154)

• X₂₁₇₃ = crosssum of X_i and X_j for these (i,j): (1, 2173), (9, 758)

• X₂₁₇₃ = X₂₃₄₉-aleph conjugate of X₂₁₇₃

• X₂₁₇₃ = crossdifference of every pair of points on line X₁X₆₅₆

• X₂₁₇₃ = isotomic conjugate of X₃₃₈₀₅

• X₂₁₇₃ = bicentric sum of PU(74)

• X₂₁₇₃ = PU(74)-harmonic conjugate of X₆₅₆