X₂₁₇₆

X₂-ISOCONJUGATE OF X₈₇

X₂₁₇₆ = isogonal conjugate of X₃₃₀

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

X₂₁₇₆ (X₂-ISOCONJUGATE OF X₈₇) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {1, 6}, {32, 101}

• Related Centers: X₃₃₀ (ISOTOMIC CONJUGATE OF X₁₉₂), X₁ (INCENTER), X₆ (SYMMEDIAN POINT), X₃₂ (3rd POWER POINT), X₁₀₁ (Ψ(INCENTER, SYMMEDIAN POINT))

Trilinears: \(a/f(a,b,c) : b/f(b,c,a) : c/f(c,a,b)\), where f(a,b,c) is as in X₈₇

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

Search Value (6, 9, 13): \(0.133520702270\)

▸ Incident Central Lines26 lines

{1, 6}, {2, 1258}, {8, 2238}, {31, 172}, {32, 101}, {39, 995}, {41, 1914}, {55, 869}, {56, 292}, {58, 2242}, {71, 2277}, {169, 1572}, {190, 194}, {239, 312}, {304, 742}, {386, 1500}, {672, 1201}, {978, 1575}, {992, 2345}, {1149, 1475}, {1185, 1621}, {1193, 1334}, {1397, 2056}, {1691, 2175}, {2174, 2304}, {2178, 2305}

▸ Functional Relations12 relations

• X₂₁₇₆ = isogonal conjugate of X₃₃₀

• X₂₁₇₆ = isotomic conjugate of X₆₃₈₃

• X₂₁₇₆ = complement of X₂₁₂₈₁

• X₂₁₇₆ = anticomplement of X₂₀₂₅₅

• X₂₁₇₆ = X_i-Ceva conjugate of X_j for these (i,j): (31, 6), (983, 55), (1423, 1403)

• X₂₁₇₆ = X_i-cross conjugate of X_j for these (i,j): (43, 6), (2209, 1403)

• X₂₁₇₆ = crosspoint of X_i and X_j for these (i,j): (31, 2209), (43, 1423), (101, 1016)

• X₂₁₇₆ = crosssum of X_i and X_j for these (i,j): (2, 1278), (87, 2319), (514, 1015)

• X₂₁₇₆ = X₉₂-isoconjugate of X₂₃₀₈₆

• X₂₁₇₆ = {X₁,X₉}-harmonic conjugate of X₁₁₀₇

• X₂₁₇₆ = crossdifference of every pair of points on line X₅₁₃X₃₇₁₆

• X₂₁₇₆ = pole wrt circumcircle of line X₆₆₇X₇₈₈