X₂₁₈₃

X₂-ISOCONJUGATE OF X₁₀₄

X₂₁₈₃ = crossdifference of every pair of points on line X₁X₅₂₂

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

X₂₁₈₃ (X₂-ISOCONJUGATE OF X₁₀₄) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {4, 9}, {6, 41}

• Related Centers: X₄ (ORTHOCENTER), X₉ (MITTENPUNKT), X₆ (SYMMEDIAN POINT), X₄₁ (-CEVA CONJUGATE OF X₃₁)

Trilinears: \((a - c) \cos B + (a - b) \cos C : :\)

Barycentrics: \(a^{2}/f(a,b,c) : b^{2}/f(b,c,a): c^{2}/f(c,a,b)\)

Search Value (6, 9, 13): \(-3.959112052001\)

▸ Alternate Coordinates2 forms

• Trilinears: \((\tan A + \tan B + \tan C) \sec A - (\sec A + \sec B + \sec C) \tan A : :\)

• Trilinears: \(a/f(a,b,c) : b/f(b,c,a) : c/f(c,a,b)\), where f(a,b,c) is as in X₁₀₄

▸ Incident Central Lines31 lines

{1, 957}, {3, 2267}, {4, 9}, {6, 41}, {25, 212}, {31, 197}, {36, 909}, {37, 1953}, {44, 513}, {45, 1334}, {51, 228}, {101, 953}, {201, 1829}, {213, 2288}, {219, 945}, {226, 1730}, {294, 1937}, {374, 1212}, {478, 2199}, {511, 1818}, {515, 2250}, {579, 610}, {674, 2340}, {937, 2215}, {1018, 2325}, {1167, 1474}, {1195, 2180}, {1253, 1486}, {1696, 2256}, {1708, 1763}, {1738, 1756}

▸ Functional Relations7 relations

• X₂₁₈₃ = isogonal conjugate of X₃₄₂₃₄

• X₂₁₈₃ = X_i-Ceva conjugate of X_j for these (i,j): (36, 902), (80, 42), (102, 55), (1465, 1457), (2222, 663), (2316, 6)

• X₂₁₈₃ = crosspoint of X_i and X_j for these (i,j): (6, 2161), (19, 913), (57, 106), (517, 1465), (901, 1262), (908, 1785)

• X₂₁₈₃ = crosssum of X_i and X_j for these (i,j): (1, 2183), (2, 3218), (9, 519), (57, 34050), (63, 914), (649, 1647), (900, 1146), (909, 1795), (4466,4707

• X₂₁₈₃ = polar conjugate of isotomic conjugate of X₂₂₃₅₀

• X₂₁₈₃ = crossdifference of every pair of points on line X₁X₅₂₂

• X₂₁₈₃ = X₉₂-isoconjugate of X₁₇₉₅