X₂₁₇₁

X₂-ISOCONJUGATE OF X₆₀

X₂₁₇₁ = isogonal conjugate of X₂₁₈₅

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

X₂₁₇₁ (X₂-ISOCONJUGATE OF X₆₀) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {19, 41}, {37, 65}

• Related Centers: X₂₁₈₅ (-ISOCONJUGATE OF X₁₈₁), X₁₉ (CLAWSON POINT), X₄₁ (-CEVA CONJUGATE OF X₃₁), X₃₇ (CROSSPOINT OF INCENTER AND CENTROID), X₆₅ (ORTHOCENTER OF THE INTOUCH TRIANGLE)

Trilinears: \(a/f(a,b,c) : b/f(b,c,a) : c/f(c,a,b)\), where f(a,b,c) is as in X₆₀

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

Search Value (6, 9, 13): \(0.727152881055\)

▸ Alternate Coordinates1 form

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

▸ Incident Central Lines23 lines

{1, 572}, {6, 1411}, {7, 192}, {9, 1405}, {12, 594}, {19, 41}, {37, 65}, {42, 1824}, {57, 1255}, {101, 1781}, {172, 1950}, {181, 756}, {226, 306}, {312, 1240}, {517, 2269}, {894, 1959}, {1100, 1404}, {1108, 1475}, {1254, 1500}, {1402, 1962}, {1841, 1887}, {2173, 2174}, {2262, 2347}

▸ Functional Relations8 relations

• X₂₁₇₁ = isogonal conjugate of X₂₁₈₅

• X₂₁₇₁ = complement of X₂₁₂₇₃

• X₂₁₇₁ = anticomplement of X₂₁₂₃₃

• X₂₁₇₁ = X_i-Ceva conjugate of X_j for these (i,j): (12, 756), (37, 2197), (65, 181), (226, 12)

• X₂₁₇₁ = cevapoint of X₁₈₁ and X₁₅₀₀

• X₂₁₇₁ = X_i-cross conjugate of X_j for these (i,j): (115, 661), (181, 1254), (1500, 756)

• X₂₁₇₁ = crosspoint of X_i and X_j for these (i,j): (1, 2051), (37, 1826), (65, 226)

• X₂₁₇₁ = crosssum of X_i and X_j for these (i,j): (1, 572), (2, 284), (81, 1790)