X₂₁₇₀

X₂-ISOCONJUGATE OF X₅₉

X₂₁₇₀ = cevapoint of X₁ and X₁₀₅₃

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

X₂₁₇₀ (X₂-ISOCONJUGATE OF X₅₉) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {1, 41}, {37, 374}

• Related Centers: X₁ (INCENTER), X₄₁ (-CEVA CONJUGATE OF X₃₁), X₃₇ (CROSSPOINT OF INCENTER AND CENTROID), X₃₇₄ (CENTROID OF THE PEDAL TRIANGLE OF X)

Trilinears: \(a/f(a,b,c) : b/f(b,c,a) : c/f(c,a,b)\), where f(a,b,c) is as in X₅₉

Barycentrics: \(a^{2} \sin^{2}(B/2 - C/2) : :\)

Search Value (6, 9, 13): \(1.960539060807\)

▸ Alternate Coordinates1 form

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

▸ Incident Central Lines32 lines

{1, 41}, {6, 1411}, {9, 644}, {11, 1146}, {19, 604}, {31, 1572}, {37, 374}, {57, 934}, {65, 1475}, {115, 661}, {163, 759}, {218, 1482}, {220, 2098}, {239, 1959}, {244, 665}, {354, 1200}, {514, 1111}, {517, 672}, {664, 673}, {756, 1573}, {910, 1055}, {926, 2310}, {1086, 1358}, {1100, 2264}, {1107, 2292}, {1108, 1400}, {1195, 2260}, {1212, 1334}, {1404, 2182}, {1731, 2323}, {1870, 2202}, {1914, 1951}

▸ Functional Relations11 relations

• X₂₁₇₀ = isogonal conjugate of X₄₅₆₄

• X₂₁₇₀ = complement of X₂₁₂₇₂

• X₂₁₇₀ = anticomplement of X₂₁₂₃₂

• X₂₁₇₀ = X_i-Ceva conjugate of X_j for these (i,j): (1, 663), (6, 661), (9, 650), (11, 2310), (19, 649), (57, 513), (312, 522), (673, 2254), (1086, 244), (1751, 656), (2006, 1769), (2161, 1635), (2217, 667)

• X₂₁₇₀ = cevapoint of X₁ and X₁₀₅₃

• X₂₁₇₀ = crosspoint of X_i and X_j for these (i,j): (1, 514), (9, 650), (11, 1086), (57, 513), (312, 522), (1022, 1168), (2590, 2591)

• X₂₁₇₀ = crosssum of X_i and X_j for these (i,j): (1, 101), (9, 100), (57, 651), (59, 1252), (63, 1813), (78, 644), (109, 604), (214, 1023), (1331, 2289)

• X₂₁₇₀ = crossdifference of every pair of points on line X₁₀₀X₃₇₃₈ (the tangent at X₁₀₀ to the circumconic centered at X₁, conic {{A, B, C,X₁₀₀,X₆₆₄,X₁₁₂₀,X₁₃₂₀}})

• X₂₁₇₀ = intersection of tangents to Steiner inellipse at X₁₀₁₅ and X₁₁₄₆

• X₂₁₇₀ = crosspoint wrt medial triangle of X₁₀₁₅ and X₁₁₄₆

• X₂₁₇₀ = barycentric square of X₆₇₂₈