X₂₁₉₄

X₂-ISOCONJUGATE OF X₂₂₆

X₂₁₉₄ = isogonal conjugate of X₁₄₄₁

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

X₂₁₉₄ (X₂-ISOCONJUGATE OF X₂₂₆) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {6, 25}, {31, 48}

• Related Centers: X₁₄₄₁ (-BETH CONJUGATE OF X₃₁₃), X₆ (SYMMEDIAN POINT), X₂₅ (HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES), X₃₁ (2nd POWER POINT), X₄₈ (CROSSPOINT OF X₁ AND X₆₃)

Trilinears: \(a/f(a,b,c) : b/f(b,c,a) : c/f(c,a,b)\), where f(a,b,c) is as in X₂₂₆

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

Search Value (6, 9, 13): \(1.486310709045\)

▸ Incident Central Lines29 lines

{1, 1762}, {3, 1779}, {6, 25}, {19, 2219}, {21, 60}, {27, 1836}, {28, 65}, {29, 1837}, {31, 48}, {41, 212}, {42, 692}, {55, 219}, {56, 58}, {81, 105}, {199, 2245}, {210, 2287}, {228, 2174}, {283, 1036}, {904, 2210}, {1011, 2278}, {1155, 1817}, {1172, 1859}, {1185, 1501}, {1396, 1456}, {1415, 1949}, {1834, 1884}, {2150, 2193}, {2192, 2332}, {2260, 2308}

▸ Functional Relations7 relations

• X₂₁₉₄ = isogonal conjugate of X₁₄₄₁

• X₂₁₉₄ = X_i-Ceva conjugate of X_j for these (i,j): (21, 2193), (1169, 32), (1172, 2204), (1175, 6)

• X₂₁₉₄ = cevapoint of X_i and X_j for these (i,j): (31, 184), (41, 2175)

• X₂₁₉₄ = X_i-cross conjugate of X_j for these (i,j): (31, 2299), (41, 284), (663, 692)

• X₂₁₉₄ = crosspoint of X_i and X_j for these (i,j): (21, 1172), (58, 284), (60, 2150)

• X₂₁₉₄ = crosssum of X_i and X_j for these (i,j): (1, 1762), (2, 2475), (10, 226), (65, 1214)

• X₂₁₉₄ = X₉₂-isoconjugate of X₁₂₁₄