X₂₁₇₄

X₂-ISOCONJUGATE OF X₇₉

X₂₁₇₄ = isogonal conjugate of X₃₀₆₉₀

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

X₂₁₇₄ (X₂-ISOCONJUGATE OF X₇₉) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {6, 41}, {37, 101}

• Related Centers: X₆ (SYMMEDIAN POINT), X₄₁ (-CEVA CONJUGATE OF X₃₁), X₃₇ (CROSSPOINT OF INCENTER AND CENTROID), 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 X₇₉

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

Search Value (6, 9, 13): \(2.527327395107\)

▸ Alternate Coordinates1 form

• Trilinears: \(g(A,B,C) : g(B,C,A) : g(C,A,B)\), where \(g(A, B, C) = \sin A + \sin 2A\)

▸ Incident Central Lines27 lines

{1, 584}, {6, 41}, {9, 2278}, {36, 583}, {37, 101}, {44, 572}, {45, 2268}, {50, 1399}, {53, 2202}, {55, 2164}, {65, 2160}, {71, 1030}, {199, 209}, {213, 1333}, {220, 2289}, {228, 2194}, {560, 869}, {594, 2329}, {662, 894}, {872, 922}, {910, 1630}, {1409, 1415}, {1964, 2210}, {2171, 2173}, {2176, 2304}, {2220, 2251}, {2264, 2302}

▸ Functional Relations6 relations

• X₂₁₇₄ = isogonal conjugate of X₃₀₆₉₀

• X₂₁₇₄ = complement of X₂₁₂₇₆

• X₂₁₇₄ = anticomplement of X₂₁₂₃₆

• X₂₁₇₄ = X_i-Ceva conjugate of X_j for these (i,j): (80, 2361), (1126, 31), (2003, 1399), (2259, 6)

• X₂₁₇₄ = crosspoint of X₃₅ and X₂₀₀₃

• X₂₁₇₄ = crossdifference of every pair of points on line X₅₂₂X₄₈₂₃ (the polar wrt polar circle of X₆₁₉₈)