X₂₂₉₇

X₂-ISOCONJUGATE OF X₁₁₉₁

X₂₂₉₇ = isogonal conjugate of X₂₉₉₉

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

X₂₂₉₇ (X₂-ISOCONJUGATE OF X₁₁₉₁) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {9, 56}, {6, 200}

• Related Centers: X₂₉₉₉ (DANNEELS-BEVAN HOMOTHETIC CENTER), X₉ (MITTENPUNKT), X₅₆ (EXSIMILICENTER), X₆ (SYMMEDIAN POINT), X₂₀₀ (-CEVA CONJUGATE OF X₉)

Trilinears: \(a/f(a,b,c) : b/f(b,c,a) : c/f(c,a,b)\), where f(a,b,c) is as in X₁₁₉₁

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

Search Value (6, 9, 13): \(2.457632429141\)

X₂₂₉₇ lies on the conic {{A, B, C,X₁,X₆}}.

▸ Incident Central Lines27 lines

{1, 346}, {2, 269}, {6, 200}, {9, 56}, {10, 937}, {34, 281}, {37, 3445}, {58, 936}, {87, 5268}, {106, 3731}, {282, 1413}, {391, 8580}, {894, 4328}, {966, 8568}, {1126, 6765}, {1438, 2268}, {1449, 2334}, {1474, 2267}, {2163, 3973}, {2256, 4936}, {2257, 5782}, {2345, 4853}, {2999, 3618}, {4334, 5296}, {5018, 5199}, {5272, 7194}, {7175, 7308}

▸ Functional Relations5 relations

• X₂₂₉₇ = isogonal conjugate of X₂₉₉₉

• X₂₂₉₇ = cevapoint of XX_i and X_j for these {i,j}: {1, 8580}, {9, 1449}, {2484, 3248}

• X₂₂₉₇ = X_i-cross conguate of X_j for these (i,j): (612, 1), (7050, 7091)

• X₂₂₉₇ = trilinear pole of the line X₆₄₉X₃₉₀₀

• X₂₂₉₇ = X_i-isoconjugate of X_j for these {i,j}: {1, 2999}, {2, 1191}, {6, 3672}, {57, 1697}, {58, 4656}, {81, 4646}, {100, 8712}, {668, 8662}