X₆₇₁

TRILINEAR POLE OF LINE X₂X_523

X₆₇₁ = polar conjugate of X₄₆₈

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

X₆₇₁ (TRILINEAR POLE OF LINE X₂X_523) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {2, 99}, {30, 98}

• Related Centers: X₂ (CENTROID), X₉₉ (STEINER POINT), X₃₀ (EULER INFINITY POINT), X₉₈ (TARRY POINT)

Trilinears: \(1/[a(2a^{2} - b^{2} - c^{2})] : :\)

Barycentrics: \((a^{2} + b^{2} - 2 c^{2}) \cdot (a^{2} - 2 b^{2} + c^{2}) : :\)

Search Value (6, 9, 13): \(1.820008131329\)

▸ Linear Combinations1 combination

• X₆₇₁ = \(5\) X₂ - \(4\) X₆₂₀, \(3\) X₂ - \(4\) X₅₄₆₁, \(7\) X₂ - \(8\) X₆₇₂₂, \(3\) X₂ + X₈₅₉₆, \(2\) X₂ - \(3\) X₉₁₆₆, \(7\) X₂ - \(6\) X₉₁₆₇, \(4\) X₂ - \(5\) X₁₄₀₆₁, \(5\) X₂ - \(6\) X₁₄₉₇₁, \(5\) X₂ - \(2\) X₁₅₃₀₀, \(5\) X₂ - X₂₀₀₉₄, \(9\) X₂ - \(8\) X₂₂₂₄₇, \(11\) X₂ - \(10\) X₃₁₂₇₄, \(13\) X₂ - \(8\) X₃₅₀₂₂, \(7\) X₂ + X₃₅₃₆₉, \(7\) X₂ - \(4\) X₃₆₅₂₁, X₂ - \(4\) X₃₆₅₂₃, \(4\) X₂ - \(3\) X₄₁₁₃₄, X₂ - \(3\) X₄₁₁₃₅, X₂ + \(8\) X₄₁₁₄₇, \(23\) X₂ - \(32\) X₄₁₁₄₈, \(7\) X₂ - \(16\) X₄₁₁₅₄, \(2\) X₄ + X₃₈₆₆₄, X₄ - \(4\) X₃₈₇₃₄, \(4\) X₅ - \(3\) X₂₃₂₃₄, \(4\) X₅ - X₂₃₂₃₅, \(3\) X₆ - \(2\) X₈₇₈₇, \(3\) X₆ - X₁₀₄₈₈, \(4\) X₆ - X₄₅₀₁₈, X₂₀ - \(4\) X₁₁₆₂₃, X₉₈ + \(2\) X₆₃₂₁, \(2\) X₉₈ + X₁₀₇₂₃, \(3\) X₉₈ - \(2\) X₁₄₈₃₀, \(5\) X₉₈ - \(2\) X₃₈₇₄₁, X₉₉ - \(4\) X₁₁₅, X₉₉ + \(2\) X₁₄₈, \(5\) X₉₉ - \(8\) X₆₂₀, \(3\) X₉₉ - \(4\) X₂₄₈₂, \(3\) X₉₉ - \(8\) X₅₄₆₁, \(7\) X₉₉ - \(16\) X₆₇₂₂, \(3\) X₉₉ - \(2\) X₈₅₉₁, \(3\) X₉₉ + \(2\) X₈₅₉₆, X₉₉ - \(3\) X₉₁₆₆, \(7\) X₉₉ - \(12\) X₉₁₆₇, \(2\) X₉₉ - \(5\) X₁₄₀₆₁, \(5\) X₉₉ - \(12\) X₁₄₉₇₁, \(5\) X₉₉ - \(4\) X₁₅₃₀₀, \(5\) X₉₉ - \(2\) X₂₀₀₉₄, \(9\) X₉₉ - \(16\) X₂₂₂₄₇, \(11\) X₉₉ - \(20\) X₃₁₂₇₄, \(13\) X₉₉ - \(16\) X₃₅₀₂₂, \(7\) X₉₉ + \(2\) X₃₅₃₆₉, \(7\) X₉₉ - \(8\) X₃₆₅₂₁, X₉₉ - \(8\) X₃₆₅₂₃, \(2\) X₉₉ - \(3\) X₄₁₁₃₄, X₉₉ - \(6\) X₄₁₁₃₅, X₉₉ + \(16\) X₄₁₁₄₇, \(23\) X₉₉ - \(64\) X₄₁₁₄₈, \(7\) X₉₉ - \(32\) X₄₁₁₅₄, \(2\) X₁₁₄ - \(3\) X₃₅₄₅, \(2\) X₁₁₅ + X₁₄₈, \(5\) X₁₁₅ - \(2\) X₆₂₀, \(3\) X₁₁₅ - X₂₄₈₂, \(3\) X₁₁₅ - \(2\) X₅₄₆₁, \(7\) X₁₁₅ - \(4\) X₆₇₂₂, \(6\) X₁₁₅ - X₈₅₉₁, \(6\) X₁₁₅ + X₈₅₉₆, \(4\) X₁₁₅ - \(3\) X₉₁₆₆, \(7\) X₁₁₅ - \(3\) X₉₁₆₇, \(8\) X₁₁₅ - \(5\) X₁₄₀₆₁, \(5\) X₁₁₅ - \(3\) X₁₄₉₇₁, \(5\) X₁₁₅ - X₁₅₃₀₀, \(10\) X₁₁₅ - X₂₀₀₉₄, \(9\) X₁₁₅ - \(4\) X₂₂₂₄₇, \(11\) X₁₁₅ - \(5\) X₃₁₂₇₄, \(13\) X₁₁₅ - \(4\) X₃₅₀₂₂, \(14\) X₁₁₅ + X₃₅₃₆₉, \(7\) X₁₁₅ - \(2\) X₃₆₅₂₁, \(8\) X₁₁₅ - \(3\) X₄₁₁₃₄, \(2\) X₁₁₅ - \(3\) X₄₁₁₃₅, X₁₁₅ + \(4\) X₄₁₁₄₇, \(23\) X₁₁₅ - \(16\) X₄₁₁₄₈, \(7\) X₁₁₅ - \(8\) X₄₁₁₅₄, X₁₄₇ - \(3\) X₃₈₃₉, \(5\) X₁₄₈ + \(4\) X₆₂₀, \(3\) X₁₄₈ + \(2\) X₂₄₈₂, \(3\) X₁₄₈ + \(4\) X₅₄₆₁, \(7\) X₁₄₈ + \(8\) X₆₇₂₂, \(3\) X₁₄₈ + X₈₅₉₁, \(3\) X₁₄₈ - X₈₅₉₆, \(2\) X₁₄₈ + \(3\) X₉₁₆₆, \(7\) X₁₄₈ + \(6\) X₉₁₆₇, \(4\) X₁₄₈ + \(5\) X₁₄₀₆₁, \(5\) X₁₄₈ + \(6\) X₁₄₉₇₁, \(5\) X₁₄₈ + \(2\) X₁₅₃₀₀, \(5\) X₁₄₈ + X₂₀₀₉₄, \(9\) X₁₄₈ + \(8\) X₂₂₂₄₇, \(11\) X₁₄₈ + \(10\) X₃₁₂₇₄, \(13\) X₁₄₈ + \(8\) X₃₅₀₂₂, \(7\) X₁₄₈ - X₃₅₃₆₉, \(7\) X₁₄₈ + \(4\) X₃₆₅₂₁, X₁₄₈ + \(4\) X₃₆₅₂₃, \(4\) X₁₄₈ + \(3\) X₄₁₁₃₄, X₁₄₈ + \(3\) X₄₁₁₃₅, X₁₄₈ - \(8\) X₄₁₁₄₇, \(23\) X₁₄₈ + \(32\) X₄₁₁₄₈, \(7\) X₁₄₈ + \(16\) X₄₁₁₅₄, \(2\) X₁₈₇ - \(3\) X₈₈₅₉, \(4\) X₂₃₀ - \(3\) X₂₆₆₁₃, X₃₇₆ - \(3\) X₁₄₆₅₁, \(2\) X₃₇₆ - \(3\) X₃₄₄₇₃, \(2\) X₃₈₁ - \(3\) X₁₄₆₃₉, \(3\) X₃₈₁ - \(2\) X₂₂₅₆₆, X₃₈₁ - \(3\) X₃₈₇₃₂, \(5\) X₃₈₁ - \(3\) X₃₈₇₄₃, X₃₈₅ - \(4\) X₃₂₄₅₇, \(4\) X₅₄₇ - \(3\) X₁₅₅₆₁, \(2\) X₅₄₇ - \(3\) X₃₈₂₂₉, \(4\) X₅₄₉ - \(3\) X₂₁₁₆₆, \(2\) X₅₄₉ - \(3\) X₃₈₂₂₄, \(2\) X₅₅₁ - \(3\) X₃₈₂₂₀, \(4\) X₅₉₇ - \(3\) X₅₁₈₂, \(2\) X₅₉₇ - \(3\) X₆₀₃₄, \(2\) X₆₁₈ - \(3\) X₂₂₄₉₀, \(2\) X₆₁₉ - \(3\) X₂₂₄₈₉, \(6\) X₆₂₀ - \(5\) X₂₄₈₂, \(3\) X₆₂₀ - \(5\) X₅₄₆₁, \(7\) X₆₂₀ - \(10\) X₆₇₂₂, \(12\) X₆₂₀ - \(5\) X₈₅₉₁, \(12\) X₆₂₀ + \(5\) X₈₅₉₆, \(8\) X₆₂₀ - \(15\) X₉₁₆₆, \(14\) X₆₂₀ - \(15\) X₉₁₆₇, \(16\) X₆₂₀ - \(25\) X₁₄₀₆₁, \(2\) X₆₂₀ - \(3\) X₁₄₉₇₁, \(4\) X₆₂₀ - X₂₀₀₉₄, \(9\) X₆₂₀ - \(10\) X₂₂₂₄₇, \(22\) X₆₂₀ - \(25\) X₃₁₂₇₄, \(13\) X₆₂₀ - \(10\) X₃₅₀₂₂, \(28\) X₆₂₀ + \(5\) X₃₅₃₆₉, \(7\) X₆₂₀ - \(5\) X₃₆₅₂₁, X₆₂₀ - \(5\) X₃₆₅₂₃, \(16\) X₆₂₀ - \(15\) X₄₁₁₃₄, \(4\) X₆₂₀ - \(15\) X₄₁₁₃₅, X₆₂₀ + \(10\) X₄₁₁₄₇, \(23\) X₆₂₀ - \(40\) X₄₁₁₄₈, \(7\) X₆₂₀ - \(20\) X₄₁₁₅₄, \(5\) X₆₃₁ - \(2\) X₁₀₉₉₂, \(5\) X₆₃₁ - \(8\) X₂₀₃₉₈, \(2\) X₈₉₂ - \(3\) X₃₉₀₆₁, \(7\) X₂₄₈₂ - \(12\) X₆₇₂₂, \(2\) X₂₄₈₂ + X₈₅₉₆, \(4\) X₂₄₈₂ - \(9\) X₉₁₆₆, \(7\) X₂₄₈₂ - \(9\) X₉₁₆₇, \(8\) X₂₄₈₂ - \(15\) X₁₄₀₆₁, \(5\) X₂₄₈₂ - \(9\) X₁₄₉₇₁, \(5\) X₂₄₈₂ - \(3\) X₁₅₃₀₀, \(10\) X₂₄₈₂ - \(3\) X₂₀₀₉₄, \(3\) X₂₄₈₂ - \(4\) X₂₂₂₄₇, \(11\) X₂₄₈₂ - \(15\) X₃₁₂₇₄, \(13\) X₂₄₈₂ - \(12\) X₃₅₀₂₂, \(14\) X₂₄₈₂ + \(3\) X₃₅₃₆₉, \(7\) X₂₄₈₂ - \(6\) X₃₆₅₂₁, X₂₄₈₂ - \(6\) X₃₆₅₂₃, \(8\) X₂₄₈₂ - \(9\) X₄₁₁₃₄, \(2\) X₂₄₈₂ - \(9\) X₄₁₁₃₅, X₂₄₈₂ + \(12\) X₄₁₁₄₇, \(23\) X₂₄₈₂ - \(48\) X₄₁₁₄₈, \(7\) X₂₄₈₂ - \(24\) X₄₁₁₅₄, \(5\) X₃₀₉₁ - \(2\) X₁₄₉₈₁, X₃₁₄₆ + \(2\) X₁₀₉₉₁, \(7\) X₃₅₂₃ - \(10\) X₃₈₇₄₀, \(3\) X₃₅₂₄ - \(4\) X₆₀₃₆, \(3\) X₃₅₂₄ - X₁₃₁₇₂, \(5\) X₃₆₁₈ - \(2\) X₁₄₉₂₈, \(7\) X₃₈₃₂ - \(4\) X₃₈₇₄₅, X₄₅₉₀ - \(4\) X₃₁₆₄₄, \(3\) X₄₅₉₀ - \(4\) X₄₄₃₉₇, \(3\) X₅₀₃₂ - \(2\) X₅₄₇₇, \(3\) X₅₀₅₄ - \(2\) X₃₃₈₁₃, \(3\) X₅₀₅₅ - X₁₃₁₈₈, \(11\) X₅₀₅₆ - \(8\) X₂₀₃₉₉, \(13\) X₅₀₆₇ - \(10\) X₃₈₇₅₁, \(5\) X₅₀₇₁ - \(6\) X₂₃₅₁₄, \(5\) X₅₀₇₆ + \(4\) X₃₈₆₂₇, \(13\) X₅₀₇₉ - \(4\) X₃₈₆₂₈, \(3\) X₅₂₁₅ - \(2\) X₃₂₄₅₆, \(2\) X₅₄₅₉ - \(3\) X₅₄₇₀, \(2\) X₅₄₅₉ + X₂₂₅₇₈, \(2\) X₅₄₆₀ - \(3\) X₅₄₆₉, \(2\) X₅₄₆₀ + X₂₂₅₇₇, \(7\) X₅₄₆₁ - \(6\) X₆₇₂₂, \(4\) X₅₄₆₁ - X₈₅₉₁, \(4\) X₅₄₆₁ + X₈₅₉₆, \(8\) X₅₄₆₁ - \(9\) X₉₁₆₆, \(14\) X₅₄₆₁ - \(9\) X₉₁₆₇, \(16\) X₅₄₆₁ - \(15\) X₁₄₀₆₁, \(10\) X₅₄₆₁ - \(9\) X₁₄₉₇₁, \(10\) X₅₄₆₁ - \(3\) X₁₅₃₀₀, \(20\) X₅₄₆₁ - \(3\) X₂₀₀₉₄, \(3\) X₅₄₆₁ - \(2\) X₂₂₂₄₇, \(22\) X₅₄₆₁ - \(15\) X₃₁₂₇₄, \(13\) X₅₄₆₁ - \(6\) X₃₅₀₂₂, \(28\) X₅₄₆₁ + \(3\) X₃₅₃₆₉, \(7\) X₅₄₆₁ - \(3\) X₃₆₅₂₁, X₅₄₆₁ - \(3\) X₃₆₅₂₃, \(16\) X₅₄₆₁ - \(9\) X₄₁₁₃₄, \(4\) X₅₄₆₁ - \(9\) X₄₁₁₃₅, X₅₄₆₁ + \(6\) X₄₁₁₄₇, \(23\) X₅₄₆₁ - \(24\) X₄₁₁₄₈, \(7\) X₅₄₆₁ - \(12\) X₄₁₁₅₄, X₅₄₆₃ - \(3\) X₅₄₆₉, X₅₄₆₄ - \(3\) X₅₄₇₀, \(3\) X₅₄₆₉ + X₂₂₅₇₇, \(3\) X₅₄₇₀ + X₂₂₅₇₈, X₅₉₈₄ + \(2\) X₃₉₈₃₈, \(4\) X₆₀₃₆ - X₁₃₁₇₂, X₆₀₅₄ - \(3\) X₁₄₆₃₉, \(3\) X₆₀₅₄ - \(4\) X₂₂₅₆₆, X₆₀₅₄ - \(6\) X₃₈₇₃₂, \(5\) X₆₀₅₄ - \(6\) X₃₈₇₄₃, \(2\) X₆₀₅₅ - \(3\) X₁₄₆₅₁, \(4\) X₆₀₅₅ - \(3\) X₃₄₄₇₃, \(2\) X₆₀₇₁ + X₃₁₅₁₃, \(4\) X₆₃₂₁ - X₁₀₇₂₃, \(3\) X₆₃₂₁ + X₁₄₈₃₀, \(5\) X₆₃₂₁ + X₃₈₇₄₁, \(2\) X₆₃₉₀ - \(3\) X₄₁₁₃₃, \(24\) X₆₇₂₂ - \(7\) X₈₅₉₁, \(24\) X₆₇₂₂ + \(7\) X₈₅₉₆, \(16\) X₆₇₂₂ - \(21\) X₉₁₆₆, \(4\) X₆₇₂₂ - \(3\) X₉₁₆₇, \(32\) X₆₇₂₂ - \(35\) X₁₄₀₆₁, \(20\) X₆₇₂₂ - \(21\) X₁₄₉₇₁, \(20\) X₆₇₂₂ - \(7\) X₁₅₃₀₀, \(40\) X₆₇₂₂ - \(7\) X₂₀₀₉₄, \(9\) X₆₇₂₂ - \(7\) X₂₂₂₄₇, \(44\) X₆₇₂₂ - \(35\) X₃₁₂₇₄, \(13\) X₆₇₂₂ - \(7\) X₃₅₀₂₂, \(8\) X₆₇₂₂ + X₃₅₃₆₉, \(2\) X₆₇₂₂ - \(7\) X₃₆₅₂₃, \(32\) X₆₇₂₂ - \(21\) X₄₁₁₃₄, \(8\) X₆₇₂₂ - \(21\) X₄₁₁₃₅, X₆₇₂₂ + \(7\) X₄₁₁₄₇, \(23\) X₆₇₂₂ - \(28\) X₄₁₁₄₈, \(3\) X₇₆₁₅ - X₉₈₉₀, \(3\) X₇₇₉₉ - \(4\) X₂₂₁₁₀, \(3\) X₇₈₀₉ - \(2\) X₇₈₄₀, \(3\) X₇₈₀₉ - \(4\) X₃₁₁₇₃, X₇₈₀₉ - \(4\) X₃₉₅₆₃, \(2\) X₇₈₁₃ - \(3\) X₄₁₁₃₆, X₇₈₄₀ - \(3\) X₁₄₀₄₁, X₇₈₄₀ - \(6\) X₃₉₅₆₃, X₇₉₈₃ - \(4\) X₁₁₅₉₉, X₇₉₈₃ + \(2\) X₁₃₁₇₈, \(2\) X₈₃₅₂ + X₁₁₀₅₄, \(4\) X₈₃₅₅ - \(3\) X₄₁₁₃₃, \(2\) X₈₅₉₁ - \(9\) X₉₁₆₆, \(7\) X₈₅₉₁ - \(18\) X₉₁₆₇, \(4\) X₈₅₉₁ - \(15\) X₁₄₀₆₁, \(5\) X₈₅₉₁ - \(18\) X₁₄₉₇₁, \(5\) X₈₅₉₁ - \(6\) X₁₅₃₀₀, \(5\) X₈₅₉₁ - \(3\) X₂₀₀₉₄, \(3\) X₈₅₉₁ - \(8\) X₂₂₂₄₇, \(11\) X₈₅₉₁ - \(30\) X₃₁₂₇₄, \(13\) X₈₅₉₁ - \(24\) X₃₅₀₂₂, \(7\) X₈₅₉₁ + \(3\) X₃₅₃₆₉, \(7\) X₈₅₉₁ - \(12\) X₃₆₅₂₁, X₈₅₉₁ - \(12\) X₃₆₅₂₃, \(4\) X₈₅₉₁ - \(9\) X₄₁₁₃₄, X₈₅₉₁ - \(9\) X₄₁₁₃₅, X₈₅₉₁ + \(24\) X₄₁₁₄₇, \(23\) X₈₅₉₁ - \(96\) X₄₁₁₄₈, \(7\) X₈₅₉₁ - \(48\) X₄₁₁₅₄, \(3\) X₈₅₉₃ - \(4\) X₈₇₈₇, \(3\) X₈₅₉₃ - \(2\) X₁₀₄₈₈, \(2\) X₈₅₉₆ + \(9\) X₉₁₆₆, \(7\) X₈₅₉₆ + \(18\) X₉₁₆₇, \(4\) X₈₅₉₆ + \(15\) X₁₄₀₆₁, \(5\) X₈₅₉₆ + \(18\) X₁₄₉₇₁, \(5\) X₈₅₉₆ + \(6\) X₁₅₃₀₀, \(5\) X₈₅₉₆ + \(3\) X₂₀₀₉₄, \(3\) X₈₅₉₆ + \(8\) X₂₂₂₄₇, \(11\) X₈₅₉₆ + \(30\) X₃₁₂₇₄, \(13\) X₈₅₉₆ + \(24\) X₃₅₀₂₂, \(7\) X₈₅₉₆ - \(3\) X₃₅₃₆₉, \(7\) X₈₅₉₆ + \(12\) X₃₆₅₂₁, X₈₅₉₆ + \(12\) X₃₆₅₂₃, \(4\) X₈₅₉₆ + \(9\) X₄₁₁₃₄, X₈₅₉₆ + \(9\) X₄₁₁₃₅, X₈₅₉₆ - \(24\) X₄₁₁₄₇, \(23\) X₈₅₉₆ + \(96\) X₄₁₁₄₈, \(7\) X₈₅₉₆ + \(48\) X₄₁₁₅₄, X₈₅₉₇ + \(4\) X₃₂₄₅₇, \(2\) X₈₅₉₈ - \(3\) X₂₆₆₁₃, \(2\) X₈₇₂₄ - \(3\) X₂₃₂₃₄, \(8\) X₈₇₈₇ - \(3\) X₄₅₀₁₈, \(3\) X₈₈₅₉ - X₉₈₅₅, X₉₁₁₄ - \(3\) X₂₂₄₈₉, X₉₁₁₆ - \(3\) X₂₂₄₉₀, \(4\) X₉₁₆₄ - \(3\) X₁₄₅₈₈, \(8\) X₉₁₆₄ - \(15\) X₄₀₄₂₉, \(7\) X₉₁₆₆ - \(4\) X₉₁₆₇, \(6\) X₉₁₆₆ - \(5\) X₁₄₀₆₁, \(5\) X₉₁₆₆ - \(4\) X₁₄₉₇₁, \(15\) X₉₁₆₆ - \(4\) X₁₅₃₀₀, \(15\) X₉₁₆₆ - \(2\) X₂₀₀₉₄, \(27\) X₉₁₆₆ - \(16\) X₂₂₂₄₇, \(33\) X₉₁₆₆ - \(20\) X₃₁₂₇₄, \(39\) X₉₁₆₆ - \(16\) X₃₅₀₂₂, \(21\) X₉₁₆₆ + \(2\) X₃₅₃₆₉, \(21\) X₉₁₆₆ - \(8\) X₃₆₅₂₁, \(3\) X₉₁₆₆ - \(8\) X₃₆₅₂₃, \(3\) X₉₁₆₆ + \(16\) X₄₁₁₄₇, \(69\) X₉₁₆₆ - \(64\) X₄₁₁₄₈, \(21\) X₉₁₆₆ - \(32\) X₄₁₁₅₄, \(24\) X₉₁₆₇ - \(35\) X₁₄₀₆₁, \(5\) X₉₁₆₇ - \(7\) X₁₄₉₇₁, \(15\) X₉₁₆₇ - \(7\) X₁₅₃₀₀, \(30\) X₉₁₆₇ - \(7\) X₂₀₀₉₄, \(27\) X₉₁₆₇ - \(28\) X₂₂₂₄₇, \(33\) X₉₁₆₇ - \(35\) X₃₁₂₇₄, \(39\) X₉₁₆₇ - \(28\) X₃₅₀₂₂, \(6\) X₉₁₆₇ + X₃₅₃₆₉, \(3\) X₉₁₆₇ - \(2\) X₃₆₅₂₁, \(3\) X₉₁₆₇ - \(14\) X₃₆₅₂₃, \(8\) X₉₁₆₇ - \(7\) X₄₁₁₃₄, \(2\) X₉₁₆₇ - \(7\) X₄₁₁₃₅, \(3\) X₉₁₆₇ + \(28\) X₄₁₁₄₇, \(69\) X₉₁₆₇ - \(112\) X₄₁₁₄₈, \(3\) X₉₁₆₇ - \(8\) X₄₁₁₅₄, \(3\) X₉₁₈₀ - \(2\) X₁₄₄₄₃, \(4\) X₉₂₉₃ + \(5\) X₄₂₃₄₅, \(2\) X₉₂₉₃ + X₄₂₅₅₃, X₉₈₆₂ + \(2\) X₃₉₈₀₉, \(2\) X₉₈₇₅ + X₉₈₈₄, X₉₈₇₅ + \(2\) X₁₂₂₅₈, \(3\) X₉₈₇₇ - \(2\) X₉₈₉₀, \(2\) X₉₈₈₀ + X₁₂₂₄₃, \(4\) X₉₈₈₀ + X₃₈₆₆₄, X₉₈₈₄ - \(4\) X₁₂₂₅₈, \(3\) X₁₀₃₀₄ - \(2\) X₃₈₇₃₈, \(4\) X₁₀₄₈₈ - \(3\) X₄₅₀₁₈, X₁₀₇₂₂ + \(2\) X₁₂₁₈₈, X₁₀₇₂₂ - \(4\) X₂₂₅₁₅, X₁₀₇₂₃ + \(4\) X₁₁₆₃₂, \(3\) X₁₀₇₂₃ + \(4\) X₁₄₈₃₀, \(5\) X₁₀₇₂₃ + \(4\) X₃₈₇₄₁, X₁₀₇₅₄ + \(2\) X₁₁₆₄₆, X₁₀₉₉₂ - \(4\) X₂₀₃₉₈, \(6\) X₁₁₅₃₉ - \(5\) X₃₈₇₅₀, \(2\) X₁₁₅₉₉ + X₁₃₁₇₈, \(3\) X₁₁₆₃₂ - X₁₄₈₃₀, \(5\) X₁₁₆₃₂ - X₃₈₇₄₁, \(2\) X₁₁₇₁₁ - \(3\) X₂₅₀₅₅, \(4\) X₁₁₇₂₅ - \(3\) X₃₈₃₁₄, \(2\) X₁₂₀₄₂ + X₃₈₇₃₃, \(4\) X₁₂₁₀₀ - \(5\) X₃₈₇₃₉, X₁₂₁₁₇ + \(2\) X₁₂₃₅₅, X₁₂₁₈₈ + \(2\) X₂₂₅₁₅, X₁₂₂₄₃ + \(4\) X₃₈₇₃₄, \(4\) X₁₂₈₃₃ - X₃₁₈₇₈, X₁₃₁₇₄ - \(3\) X₁₉₈₇₅, \(3\) X₁₄₀₄₁ - \(2\) X₃₁₁₇₃, \(25\) X₁₄₀₆₁ - \(24\) X₁₄₉₇₁, \(25\) X₁₄₀₆₁ - \(8\) X₁₅₃₀₀, \(25\) X₁₄₀₆₁ - \(4\) X₂₀₀₉₄, \(45\) X₁₄₀₆₁ - \(32\) X₂₂₂₄₇, \(11\) X₁₄₀₆₁ - \(8\) X₃₁₂₇₄, \(65\) X₁₄₀₆₁ - \(32\) X₃₅₀₂₂, \(35\) X₁₄₀₆₁ + \(4\) X₃₅₃₆₉, \(35\) X₁₄₀₆₁ - \(16\) X₃₆₅₂₁, \(5\) X₁₄₀₆₁ - \(16\) X₃₆₅₂₃, \(5\) X₁₄₀₆₁ - \(3\) X₄₁₁₃₄, \(5\) X₁₄₀₆₁ - \(12\) X₄₁₁₃₅, \(5\) X₁₄₀₆₁ + \(32\) X₄₁₁₄₇, \(115\) X₁₄₀₆₁ - \(128\) X₄₁₁₄₈, \(35\) X₁₄₀₆₁ - \(64\) X₄₁₁₅₄, \(3\) X₁₄₂₆₉ - \(2\) X₂₂₅₀₅, \(3\) X₁₄₅₆₈ - \(2\) X₂₂₃₂₉, \(2\) X₁₄₅₈₈ - \(5\) X₄₀₄₂₉, \(9\) X₁₄₆₃₉ - \(4\) X₂₂₅₆₆, \(5\) X₁₄₆₃₉ - \(2\) X₃₈₇₄₃, X₁₄₆₉₂ - \(6\) X₂₃₀₄₆, \(5\) X₁₄₈₃₀ - \(3\) X₃₈₇₄₁, \(3\) X₁₄₉₇₁ - X₁₅₃₀₀, \(6\) X₁₄₉₇₁ - X₂₀₀₉₄, \(27\) X₁₄₉₇₁ - \(20\) X₂₂₂₄₇, \(33\) X₁₄₉₇₁ - \(25\) X₃₁₂₇₄, \(39\) X₁₄₉₇₁ - \(20\) X₃₅₀₂₂, \(42\) X₁₄₉₇₁ + \(5\) X₃₅₃₆₉, \(21\) X₁₄₉₇₁ - \(10\) X₃₆₅₂₁, \(3\) X₁₄₉₇₁ - \(10\) X₃₆₅₂₃, \(8\) X₁₄₉₇₁ - \(5\) X₄₁₁₃₄, \(2\) X₁₄₉₇₁ - \(5\) X₄₁₁₃₅, \(3\) X₁₄₉₇₁ + \(20\) X₄₁₁₄₇, \(69\) X₁₄₉₇₁ - \(80\) X₄₁₁₄₈, \(21\) X₁₄₉₇₁ - \(40\) X₄₁₁₅₄, \(9\) X₁₅₃₀₀ - \(20\) X₂₂₂₄₇, \(11\) X₁₅₃₀₀ - \(25\) X₃₁₂₇₄, \(13\) X₁₅₃₀₀ - \(20\) X₃₅₀₂₂, \(14\) X₁₅₃₀₀ + \(5\) X₃₅₃₆₉, \(7\) X₁₅₃₀₀ - \(10\) X₃₆₅₂₁, X₁₅₃₀₀ - \(10\) X₃₆₅₂₃, \(8\) X₁₅₃₀₀ - \(15\) X₄₁₁₃₄, \(2\) X₁₅₃₀₀ - \(15\) X₄₁₁₃₅, X₁₅₃₀₀ + \(20\) X₄₁₁₄₇, \(23\) X₁₅₃₀₀ - \(80\) X₄₁₁₄₈, \(7\) X₁₅₃₀₀ - \(40\) X₄₁₁₅₄, \(2\) X₁₅₃₀₁ - \(5\) X₃₁₂₇₅, X₁₅₃₄₂ - \(4\) X₁₆₂₇₈, \(2\) X₁₅₆₈₆ - \(3\) X₃₈₇₄₂, \(5\) X₁₅₆₉₂ - \(6\) X₃₈₇₃₇, \(5\) X₁₅₆₉₃ - \(6\) X₂₆₆₁₄, \(5\) X₁₅₆₉₄ - \(6\) X₃₄₁₂₇, \(7\) X₁₅₇₀₂ - \(12\) X₃₈₇₃₅, \(7\) X₁₅₇₀₂ - \(6\) X₃₈₇₄₈, \(4\) X₁₇₉₄₈ - \(3\) X₃₉₀₆₁, \(3\) X₁₉₅₇₀ - X₄₄₃₆₇, \(4\) X₁₉₆₆₂ - \(3\) X₂₁₃₅₆, \(5\) X₁₉₇₀₈ - \(4\) X₃₈₇₃₆, \(9\) X₂₀₀₉₄ - \(40\) X₂₂₂₄₇, \(11\) X₂₀₀₉₄ - \(50\) X₃₁₂₇₄, \(13\) X₂₀₀₉₄ - \(40\) X₃₅₀₂₂, \(7\) X₂₀₀₉₄ + \(5\) X₃₅₃₆₉, \(7\) X₂₀₀₉₄ - \(20\) X₃₆₅₂₁, X₂₀₀₉₄ - \(20\) X₃₆₅₂₃, \(4\) X₂₀₀₉₄ - \(15\) X₄₁₁₃₄, X₂₀₀₉₄ - \(15\) X₄₁₁₃₅, X₂₀₀₉₄ + \(40\) X₄₁₁₄₇, \(23\) X₂₀₀₉₄ - \(160\) X₄₁₁₄₈, \(7\) X₂₀₀₉₄ - \(80\) X₄₁₁₅₄, X₂₀₇₇₄ - \(4\) X₃₉₁₂₀, \(2\) X₂₂₁₁₀ - \(3\) X₃₃₂₂₈, \(44\) X₂₂₂₄₇ - \(45\) X₃₁₂₇₄, \(13\) X₂₂₂₄₇ - \(9\) X₃₅₀₂₂, \(56\) X₂₂₂₄₇ + \(9\) X₃₅₃₆₉, \(14\) X₂₂₂₄₇ - \(9\) X₃₆₅₂₁, \(2\) X₂₂₂₄₇ - \(9\) X₃₆₅₂₃, \(32\) X₂₂₂₄₇ - \(27\) X₄₁₁₃₄, \(8\) X₂₂₂₄₇ - \(27\) X₄₁₁₃₅, X₂₂₂₄₇ + \(9\) X₄₁₁₄₇, \(23\) X₂₂₂₄₇ - \(36\) X₄₁₁₄₈, \(7\) X₂₂₂₄₇ - \(18\) X₄₁₁₅₄, \(3\) X₂₂₅₁₀ - \(2\) X₄₅₈₇₉, \(3\) X₂₂₅₁₁ - \(2\) X₄₅₈₈₀, \(2\) X₂₂₅₆₆ - \(9\) X₃₈₇₃₂, \(10\) X₂₂₅₆₆ - \(9\) X₃₈₇₄₃, \(3\) X₂₂₅₇₁ - X₂₂₉₉₇, \(3\) X₂₂₅₇₂ - X₂₂₉₉₈, \(3\) X₂₃₂₃₄ - X₂₃₂₃₅, X₃₁₁₇₃ - \(3\) X₃₉₅₆₃, \(65\) X₃₁₂₇₄ - \(44\) X₃₅₀₂₂, \(70\) X₃₁₂₇₄ + \(11\) X₃₅₃₆₉, \(35\) X₃₁₂₇₄ - \(22\) X₃₆₅₂₁, \(5\) X₃₁₂₇₄ - \(22\) X₃₆₅₂₃, \(40\) X₃₁₂₇₄ - \(33\) X₄₁₁₃₄, \(10\) X₃₁₂₇₄ - \(33\) X₄₁₁₃₅, \(5\) X₃₁₂₇₄ + \(44\) X₄₁₁₄₇, \(115\) X₃₁₂₇₄ - \(176\) X₄₁₁₄₈, \(35\) X₃₁₂₇₄ - \(88\) X₄₁₁₅₄, \(3\) X₃₁₆₄₄ - X₄₄₃₉₇, \(3\) X₃₁₉₉₈ - \(4\) X₃₅₀₈₇, \(3\) X₃₁₉₉₈ - \(2\) X₄₄₃₇₂, \(2\) X₃₂₄₅₉ - \(3\) X₄₁₁₃₉, \(2\) X₃₃₃₇₆ - \(3\) X₄₂₀₆₂, \(2\) X₃₃₃₇₇ - \(3\) X₄₂₀₆₃, \(4\) X₃₄₂₀₀ - \(3\) X₃₈₇₃₁, \(56\) X₃₅₀₂₂ + \(13\) X₃₅₃₆₉, \(14\) X₃₅₀₂₂ - \(13\) X₃₆₅₂₁, \(2\) X₃₅₀₂₂ - \(13\) X₃₆₅₂₃, \(32\) X₃₅₀₂₂ - \(39\) X₄₁₁₃₄, \(8\) X₃₅₀₂₂ - \(39\) X₄₁₁₃₅, X₃₅₀₂₂ + \(13\) X₄₁₁₄₇, \(23\) X₃₅₀₂₂ - \(52\) X₄₁₁₄₈, \(7\) X₃₅₀₂₂ - \(26\) X₄₁₁₅₄, \(3\) X₃₅₂₉₇ - \(4\) X₄₄₄₀₁, X₃₅₃₆₉ + \(4\) X₃₆₅₂₁, X₃₅₃₆₉ + \(28\) X₃₆₅₂₃, \(4\) X₃₅₃₆₉ + \(21\) X₄₁₁₃₄, X₃₅₃₆₉ + \(21\) X₄₁₁₃₅, X₃₅₃₆₉ - \(56\) X₄₁₁₄₇, \(23\) X₃₅₃₆₉ + \(224\) X₄₁₁₄₈, X₃₅₃₆₉ + \(16\) X₄₁₁₅₄, X₃₆₅₂₁ - \(7\) X₃₆₅₂₃, \(16\) X₃₆₅₂₁ - \(21\) X₄₁₁₃₄, \(4\) X₃₆₅₂₁ - \(21\) X₄₁₁₃₅, X₃₆₅₂₁ + \(14\) X₄₁₁₄₇, \(23\) X₃₆₅₂₁ - \(56\) X₄₁₁₄₈, X₃₆₅₂₁ - \(4\) X₄₁₁₅₄, \(16\) X₃₆₅₂₃ - \(3\) X₄₁₁₃₄, \(4\) X₃₆₅₂₃ - \(3\) X₄₁₁₃₅, X₃₆₅₂₃ + \(2\) X₄₁₁₄₇, \(23\) X₃₆₅₂₃ - \(8\) X₄₁₁₄₈, \(7\) X₃₆₅₂₃ - \(4\) X₄₁₁₅₄, \(2\) X₃₇₄₆₁ - \(3\) X₃₈₂₂₇, \(3\) X₃₈₃₃₅ - X₃₈₇₄₄, X₃₈₆₆₄ + \(8\) X₃₈₇₃₄, \(5\) X₃₈₇₃₂ - X₃₈₇₄₃, \(4\) X₃₉₈₀₆ - X₃₉₈₃₇, X₄₁₁₃₄ - \(4\) X₄₁₁₃₅, \(3\) X₄₁₁₃₄ + \(32\) X₄₁₁₄₇, \(69\) X₄₁₁₃₄ - \(128\) X₄₁₁₄₈, \(21\) X₄₁₁₃₄ - \(64\) X₄₁₁₅₄, \(3\) X₄₁₁₃₅ + \(8\) X₄₁₁₄₇, \(69\) X₄₁₁₃₅ - \(32\) X₄₁₁₄₈, \(21\) X₄₁₁₃₅ - \(16\) X₄₁₁₅₄, \(23\) X₄₁₁₄₇ + \(4\) X₄₁₁₄₈, \(7\) X₄₁₁₄₇ + \(2\) X₄₁₁₅₄, \(14\) X₄₁₁₄₈ - \(23\) X₄₁₁₅₄, \(5\) X₄₂₃₄₅ - \(2\) X₄₂₅₅₃

X₆₇₁ lies on the Kiepert circumhyperbola, Steiner circumellipse, the cubics K008, K025, K063, K185, K209, K239, K240, K241, K248, K273, K298, K299, K300, K301, K302, K303a, K303b, K304, K305, K353, K370, K565, K595, K715, K751, K809, K854, K914, K1153, the curves Q001, Q044, Q094, Q096, the Darboux septic.

▸ Incident Central Lines457 lines

{1, 9875}, {2, 99}, {3, 7607}, {4, 542}, {5, 7608}, {6, 598}, {8, 35177}, {10, 190}, {11, 12348}, {12, 12349}, {13, 531}, {14, 530}, {17, 5459}, {18, 5460}, {20, 11623}, {23, 3455}, {25, 9876}, {30, 98}, {32, 9878}, {39, 8786}, {55, 12326}, {56, 18969}, {69, 5485}, {75, 35181}, {76, 338}, {83, 597}, {94, 35139}, {110, 5465}, {114, 3545}, {125, 10556}, {140, 10185}, {141, 10302}, {147, 3839}, {183, 5077}, {187, 8587}, {193, 23334}, {194, 7775}, {226, 664}, {230, 8598}, {262, 381}, {265, 34174}, {275, 18831}, {290, 10097}, {297, 16077}, {298, 42035}, {299, 42036}, {303, 36775}, {315, 2996}, {316, 524}, {317, 34163}, {321, 668}, {325, 5503}, {371, 35699}, {372, 35698}, {376, 6055}, {382, 6179}, {384, 7817}, {385, 3849}, {395, 8595}, {396, 8594}, {402, 12347}, {458, 43530}, {485, 489}, {486, 490}, {493, 12352}, {494, 12353}, {511, 19905}, {512, 35146}, {513, 35155}, {514, 35153}, {519, 7983}, {523, 9180}, {525, 5641}, {527, 11608}, {528, 10769}, {532, 11602}, {533, 11603}, {536, 11611}, {538, 1916}, {546, 7858}, {547, 15561}, {549, 21166}, {551, 38220}, {616, 43543}, {617, 43542}, {618, 9116}, {619, 9114}, {625, 39785}, {631, 10992}, {666, 5080}, {690, 5466}, {698, 10290}, {729, 2086}, {754, 11606}, {804, 3228}, {843, 16341}, {850, 10561}, {858, 15398}, {886, 3978}, {889, 17790}, {903, 2786}, {923, 4586}, {1003, 5152}, {1007, 9741}, {1078, 7748}, {1084, 14700}, {1121, 2785}, {1131, 13639}, {1132, 13759}, {1153, 8589}, {1300, 35191}, {1327, 45420}, {1328, 45421}, {1446, 4569}, {1494, 2394}, {1499, 9487}, {1509, 23903}, {1641, 22254}, {1649, 9183}, {1975, 7870}, {1989, 39295}, {1995, 2936}, {2023, 42849}, {2052, 6528}, {2373, 39413}, {2407, 45774}, {2408, 2793}, {2444, 43668}, {2479, 24008}, {2480, 24007}, {2592, 15165}, {2593, 15164}, {2783, 10711}, {2784, 10710}, {2787, 3227}, {2792, 10709}, {2794, 3424}, {2795, 6175}, {2797, 10714}, {2798, 10715}, {2854, 16175}, {2986, 18878}, {3023, 11238}, {3027, 11237}, {3058, 13183}, {3068, 13908}, {3069, 13968}, {3091, 14981}, {3096, 18840}, {3124, 9169}, {3146, 10991}, {3316, 45509}, {3317, 45508}, {3329, 8592}, {3363, 15048}, {3399, 6248}, {3406, 12203}, {3407, 5309}, {3413, 6189}, {3414, 6190}, {3448, 10555}, {3523, 38740}, {3524, 6036}, {3534, 12042}, {3582, 10089}, {3584, 10086}, {3618, 14928}, {3629, 33698}, {3656, 7970}, {3767, 33007}, {3815, 20112}, {3830, 10722}, {3832, 38745}, {3845, 6033}, {3972, 5939}, {4080, 4555}, {4444, 18827}, {4562, 43534}, {4563, 14916}, {4590, 31644}, {4597, 16826}, {4762, 35152}, {4785, 35165}, {5007, 14042}, {5025, 7801}, {5032, 5477}, {5054, 11668}, {5055, 11669}, {5056, 20399}, {5064, 5186}, {5067, 38751}, {5071, 10155}, {5076, 38627}, {5079, 38628}, {5134, 37854}, {5189, 15899}, {5215, 32456}, {5286, 5395}, {5319, 14068}, {5392, 46134}, {5434, 13182}, {5471, 41745}, {5472, 41746}, {5476, 11170}, {5478, 41043}, {5479, 41042}, {5480, 14485}, {5523, 37765}, {5569, 17004}, {5597, 12345}, {5598, 12346}, {5976, 11287}, {5978, 31693}, {5979, 31694}, {5980, 11295}, {5981, 11296}, {5984, 39838}, {5989, 7884}, {6071, 31513}, {6094, 37859}, {6103, 40890}, {6108, 35932}, {6109, 35931}, {6114, 9762}, {6115, 9760}, {6390, 8355}, {6392, 7877}, {6539, 6540}, {6625, 33770}, {6648, 7316}, {6655, 7810}, {6656, 10159}, {6658, 7755}, {6669, 43548}, {6670, 43549}, {6777, 12817}, {6778, 12816}, {6787, 34383}, {7375, 43565}, {7376, 43564}, {7388, 10194}, {7389, 10195}, {7610, 7771}, {7668, 36165}, {7669, 37915}, {7739, 33016}, {7745, 20583}, {7746, 33274}, {7747, 34604}, {7751, 9939}, {7752, 33006}, {7753, 32528}, {7756, 34506}, {7758, 32996}, {7759, 14062}, {7763, 32984}, {7764, 32993}, {7765, 16044}, {7768, 33229}, {7770, 43527}, {7772, 33018}, {7777, 8176}, {7780, 33256}, {7781, 32966}, {7782, 11149}, {7783, 39565}, {7796, 14063}, {7799, 8781}, {7802, 33192}, {7803, 18841}, {7804, 8289}, {7811, 33017}, {7813, 41136}, {7818, 43688}, {7821, 14045}, {7825, 7917}, {7828, 8369}, {7832, 8360}, {7839, 39590}, {7842, 17129}, {7843, 14044}, {7847, 8359}, {7850, 15533}, {7851, 33237}, {7856, 14035}, {7857, 32985}, {7861, 7944}, {7865, 8782}, {7872, 31276}, {7880, 14046}, {7898, 17131}, {7903, 20105}, {7924, 9466}, {7926, 22253}, {7933, 17130}, {7937, 21358}, {7942, 8366}, {8179, 11171}, {8182, 17008}, {8288, 40877}, {8353, 13468}, {8356, 11168}, {8430, 23878}, {8584, 45103}, {8667, 11057}, {8703, 38730}, {8785, 20977}, {8982, 12297}, {9112, 41621}, {9113, 41620}, {9139, 34150}, {9141, 17708}, {9148, 17993}, {9164, 14588}, {9213, 34312}, {9227, 14724}, {9293, 42345}, {9302, 19924}, {9479, 43098}, {9698, 33024}, {9766, 11055}, {9862, 15682}, {9879, 13207}, {9909, 39832}, {10153, 27088}, {10187, 11290}, {10188, 11289}, {10304, 38738}, {10562, 31296}, {10733, 34211}, {10989, 34320}, {11001, 38749}, {11078, 36316}, {11092, 36317}, {11114, 38557}, {11140, 46139}, {11165, 15814}, {11172, 14907}, {11184, 31859}, {11539, 38750}, {11656, 17702}, {11711, 25055}, {11725, 38314}, {12040, 37647}, {12100, 38739}, {12154, 40671}, {12155, 40672}, {12156, 14537}, {12296, 14244}, {12833, 31878}, {13083, 46054}, {13084, 46053}, {13087, 35830}, {13088, 35831}, {13174, 19875}, {13180, 34612}, {13181, 34606}, {13189, 45701}, {13190, 45700}, {13273, 14612}, {13640, 13676}, {13760, 13796}, {14023, 33279}, {14269, 14488}, {14692, 23046}, {14712, 33689}, {14904, 40707}, {14905, 40706}, {14957, 36827}, {14995, 23348}, {15301, 31275}, {15534, 17503}, {15535, 20126}, {15638, 17952}, {15686, 38742}, {15692, 38737}, {15693, 26614}, {15694, 34127}, {15702, 38735}, {16041, 32833}, {16042, 34013}, {16277, 34603}, {16508, 16509}, {16922, 31652}, {17005, 39601}, {17132, 34899}, {17556, 38499}, {17577, 45964}, {17950, 35157}, {18026, 40149}, {18316, 41626}, {18800, 18842}, {18822, 40459}, {19108, 32788}, {19109, 32787}, {19662, 21356}, {19696, 35007}, {19708, 38736}, {20975, 38526}, {21849, 39846}, {22037, 35162}, {22510, 45879}, {22511, 45880}, {22735, 41143}, {23870, 43092}, {23871, 43091}, {23905, 25536}, {23942, 34016}, {24624, 36085}, {25221, 25222}, {25328, 41498}, {31160, 41142}, {31450, 33009}, {31862, 46023}, {31863, 46024}, {31998, 35087}, {32458, 32836}, {32459, 41139}, {32552, 33607}, {32553, 33606}, {32808, 42023}, {32809, 42024}, {32832, 33215}, {32982, 43681}, {32986, 42850}, {33220, 44536}, {33264, 39652}, {33285, 46236}, {33513, 39284}, {33602, 36327}, {33603, 35749}, {33604, 36331}, {33605, 35750}, {34171, 34574}, {34200, 38731}, {34289, 40814}, {34581, 37860}, {34664, 40448}, {35140, 43673}, {35142, 44427}, {35297, 44401}, {37461, 38227}, {37856, 38945}, {37940, 39854}, {37948, 39831}, {38335, 38744}, {38888, 38946}, {39229, 46082}, {39230, 46083}, {39806, 39837}, {39828, 44837}, {39842, 40178}, {40016, 42371}, {41022, 41047}, {41023, 41046}, {42738, 44552}, {44146, 46105}

▸ Functional Relations49 relations

• X₆₇₁ = midpoint of X_i and X_j for these {i,j}: {1, 9875}, {2, 148}, {3, 12355}, {4, 12243}, {316, 11054}, {385, 8597}, {895, 14833}, {3534, 38733}, {3543, 11177}, {3830, 12188}, {5463, 22577}, {5464, 22578}, {6321, 11632}, {6777, 35752}, {6778, 36330}, {8591, 8596}, {9862, 15682}, {9879, 13207}, {9882, 9883}, {10754, 11161}, {14712, 40246}, {31695, 31696}, {33432, 33433}

• X₆₇₁ = reflection of X_i in X_j for these {i,j}: {1, 12258}, {2, 115}, {4, 9880}, {98, 11632}, {99, 2}, {110, 5465}, {115, 36523}, {316, 8352}, {325, 37350}, {376, 6055}, {691, 16092}, {843, 16341}, {892, 17948}, {1649, 9183}, {2482, 5461}, {3534, 12042}, {3830, 22515}, {5182, 6034}, {5463, 5460}, {5464, 5459}, {5466, 18007}, {5978, 31693}, {5979, 31694}, {6033, 3845}, {6054, 381}, {6390, 8355}, {6722, 41154}, {7799, 33228}, {7809, 14041}, {7840, 31173}, {7970, 3656}, {8591, 2482}, {8593, 6}, {8594, 396}, {8595, 395}, {8598, 230}, {8724, 5}, {9114, 619}, {9116, 618}, {9144, 16278}, {9166, 41135}, {9855, 187}, {9877, 7615}, {9880, 38734}, {9881, 10}, {9884, 1}, {9885, 33476}, {9886, 33477}, {10488, 8787}, {10722, 3830}, {10753, 20423}, {11001, 38749}, {11006, 125}, {11152, 39}, {11161, 11646}, {12117, 3}, {12177, 5476}, {12347, 402}, {12356, 10054}, {12357, 10070}, {13640, 13676}, {13760, 13796}, {14041, 39563}, {14639, 38732}, {15300, 620}, {15342, 9144}, {15561, 38229}, {15682, 39809}, {16508, 16509}, {19911, 7617}, {20094, 15300}, {20126, 15535}, {21166, 38224}, {22568, 33461}, {22570, 33460}, {23235, 8724}, {27088, 43291}, {32469, 32447}, {33342, 13968}, {33343, 13908}, {34473, 14651}, {35705, 3363}, {35751, 32553}, {35931, 6109}, {35932, 6108}, {36329, 32552}, {36521, 6722}, {37785, 22574}, {37786, 22573}, {38664, 12243}, {38730, 8703}, {38748, 38735}, {39785, 625}, {39846, 21849}, {41042, 5479}, {41043, 5478}, {41134, 9166}, {44372, 35087}, {45018, 8593}

• X₆₇₁ = reflection of X₉₁₄₀ in the Fermat line

• X₆₇₁ = isogonal conjugate of X₁₈₇

• X₆₇₁ = isotomic conjugate of X₅₂₄

• X₆₇₁ = anticomplement of X₂₄₈₂

• X₆₇₁ = circumcircle-inverse of X(11643

• X₆₇₁ = 3rd-Lemoine-circle-(Ehrmann)-inverse of X₈₉₅

• X₆₇₁ = polar-circle-inverse of X₅₀₉₅

• X₆₇₁ = orthoptic-circle-of-Steiner-inellipe-inverse of X₉₁₇₂

• X₆₇₁ = circumcircle-of-anticomplementary-triangle-inverse of X₃₂₂₅₅

• X₆₇₁ = polar conjugate of X₄₆₈

• X₆₇₁ = antigonal image of X₂

• X₆₇₁ = symgonal image of X₂

• X₆₇₁ = cyclocevian conjugate of X₁₃₅₇₄

• X₆₇₁ = psi-transform of X₉₁₆₉

• X₆₇₁ = X_i-anticomplementary conjugate of X_j for these (i,j): {897, 14360}, {923, 8591}, {10630, 8}, {15398, 4329}, {34539, 21295}, {34574, 7192}, {36142, 44010}, {41936, 192}

• X₆₇₁ = X_i-complementary conjugate of X_j for these (i,j): {31, 39061}, {46275, 2887}

• X₆₇₁ = X_i-Ceva conjugate of X_j for these (i,j): {2, 39061}, {892, 5466}, {18023, 30786}, {46111, 17983}

• X₆₇₁ = X_i-cross conjugate of X_j for these (i,j): {6, 10415}, {67, 2373}, {69, 44182}, {111, 17983}, {316, 83}, {524, 2}, {690, 99}, {858, 264}, {895, 30786}, {1499, 39296}, {1648, 523}, {4442, 75}, {5466, 892}, {5468, 40429}, {8352, 598}, {8586, 7608}, {9134, 35136}, {9140, 1494}, {9979, 648}, {10097, 691}, {10561, 34574}, {10754, 8781}, {11054, 10302}, {11646, 98}, {14263, 10630}, {15638, 2408}, {17162, 1268}, {17491, 86}, {17497, 274}, {20977, 6}, {21298, 40415}, {23061, 40410}, {24724, 14621}, {25328, 18019}, {30709, 668}, {31125, 18023}, {33906, 37880}, {34290, 18829}, {39232, 110}, {41724, 95}, {42344, 42345}, {44915, 468}, {45291, 4590}, {46154, 111}

• X₆₇₁ = cevapoint of X_i and X_j for these (i,j): {2, 524}, {4, 5523}, {6, 23}, {111, 895}, {115, 690}, {523, 1648}, {2408, 15638}, {5468, 14588}, {13492, 14262}, {31125, 46154}, {31644, 45291}, {39229, 39230}, {42344, 42553}

• X₆₇₁ = crosspoint of X_i and X_j for these (i,j): {2, 46275}, {18023, 46111}

• X₆₇₁ = crosssum of X_i and X_j for these (i,j): {6, 46276}, {351, 21906}, {14567, 23200}

• X₆₇₁ = trilinear pole of line {2, 523}

• X₆₇₁ = crossdifference of every pair of points on line {351, 39689}

• X₆₇₁ = the point of intersection, other than A, B, and C, of the Steiner circumellipse and the Kiepert hyperbola

• X₆₇₁ = Kiepert-hyperbola-antipode of X₂

• X₆₇₁ = Steiner- circumellipse- antipode of X₉₉

• X₆₇₁ = projection from Steiner inellipse to Steiner circumellipse of X₁₁₅

• X₆₇₁ = antigonal image of X₂

• X₆₇₁ = syngonal conjugate of X₂

• X₆₇₁ = pole wrt polar circle of trilinear polar of X₄₆₈

• X₆₇₁ = Kirikami concurrent circles image of X₁₃

• X₆₇₁ = Kirikami concurrent circles image of X₁₄

• X₆₇₁ = X₃ of anti-McCay triangle

• X₆₇₁ = crossdifference of PU(107)

• X₆₇₁ = McCay-to-Artzt similarity image of X₆

• X₆₇₁ = perspector of ABC and 1st Brocard triangle of anti-McCay triangle

• X₆₇₁ = Cundy-Parry Phi transform of X₇₆₀₇

• X₆₇₁ = Cundy-Parry Psi transform of X₅₇₆

• X₆₇₁ = Steiner-circumellipse-X₁-antipode of X₃₅₁₈₀

• X₆₇₁ = Steiner-circumellipse-X₃-antipode of X₃₅₁₇₈

• X₆₇₁ = Steiner-circumellipse-X₄-antipode of X₆₄₈

• X₆₇₁ = Steiner-circumellipse-X₆-antipode of X₃₅₁₃₈

• X₆₇₁ = perspector of hyperbola {A, B, C,X₈₉₂,PU(180)}}

• X₆₇₁ = X_i-isoconjugate of X_j for these (i,j): {1, 187}, {2, 922}, {6, 896}, {19, 3292}, {31, 524}, {32, 14210}, {41, 7181}, {42, 16702}, {48, 468}, {58, 21839}, {63, 44102}, {75, 14567}, {92, 23200}, {101, 14419}, {110, 2642}, {111, 42081}, {163, 690}, {213, 6629}, {351, 662}, {512, 23889}, {560, 3266}, {604, 3712}, {661, 5467}, {669, 24039}, {692, 4750}, {798, 5468}, {810, 4235}, {897, 39689}, {904, 7267}, {923, 2482}, {1101, 1648}, {1333, 4062}, {1415, 14432}, {1580, 18872}, {1649, 36142}, {1755, 5967}, {1910, 9155}, {1911, 4760}, {1918, 16741}, {1919, 42721}, {1967, 5026}, {1973, 6390}, {2148, 41586}, {2157, 6593}, {2159, 5642}, {2173, 9717}, {2206, 42713}, {2234, 41309}, {2624, 14559}, {4575, 14273}, {4933, 28607}, {4938, 34819}, {5095, 36060}, {5477, 36051}, {7813, 46289}, {9177, 36150}, {9247, 44146}, {9406, 36890}, {14417, 32676}, {14424, 34072}, {21906, 24041}, {24038, 32740}, {30605, 34073}, {32459, 38252}, {32678, 44814}

• X₆₇₁ = barycentric product X_i*X_j for these {i,j}: {1, 46277}, {3, 46111}, {4, 30786}, {6, 18023}, {69, 17983}, {75, 897}, {76, 111}, {83, 31125}, {99, 5466}, {264, 895}, {290, 5968}, {298, 36307}, {299, 36310}, {304, 36128}, {305, 8753}, {308, 46154}, {316, 10415}, {325, 9154}, {523, 892}, {561, 923}, {598, 42008}, {599, 18818}, {648, 14977}, {670, 9178}, {691, 850}, {693, 5380}, {799, 23894}, {1236, 10422}, {1494, 9214}, {1502, 32740}, {1577, 36085}, {1969, 36060}, {2408, 35179}, {3260, 9139}, {3266, 10630}, {3596, 7316}, {5547, 6063}, {5641, 16092}, {6330, 36894}, {6331, 10097}, {8430, 43187}, {9170, 18007}, {9180, 34760}, {9213, 35139}, {10416, 14364}, {11123, 14728}, {14246, 18019}, {14609, 34087}, {14908, 18022}, {15398, 44146}, {17948, 18823}, {19626, 40362}, {20948, 36142}, {23105, 45773}, {23288, 35138}, {27808, 43926}, {32729, 44173}, {34574, 35522}, {39061, 46275}, {40016, 41272}, {40826, 42007}

• X₆₇₁ = barycentric quotient X_i/X_j for these {i,j}: {1, 896}, {2, 524}, {3, 3292}, {4, 468}, {5, 41586}, {6, 187}, {7, 7181}, {8, 3712}, {10, 4062}, {23, 6593}, {25, 44102}, {30, 5642}, {31, 922}, {32, 14567}, {37, 21839}, {67, 14357}, {69, 6390}, {74, 9717}, {75, 14210}, {76, 3266}, {81, 16702}, {86, 6629}, {94, 43084}, {98, 5967}, {99, 5468}, {110, 5467}, {111, 6}, {115, 1648}, {141, 7813}, {148, 11053}, {184, 23200}, {187, 39689}, {193, 32459}, {230, 5477}, {239, 4760}, {264, 44146}, {274, 16741}, {316, 7664}, {321, 42713}, {381, 32225}, {385, 5026}, {395, 9117}, {396, 9115}, {403, 12828}, {468, 5095}, {476, 14559}, {511, 9155}, {512, 351}, {513, 14419}, {514, 4750}, {522, 14432}, {523, 690}, {524, 2482}, {525, 14417}, {526, 44814}, {538, 45672}, {542, 45662}, {543, 1641}, {599, 39785}, {648, 4235}, {661, 2642}, {662, 23889}, {668, 42721}, {690, 1649}, {691, 110}, {694, 18872}, {729, 41309}, {799, 24039}, {804, 11183}, {826, 14424}, {850, 35522}, {858, 5181}, {892, 99}, {894, 7267}, {895, 3}, {896, 42081}, {897, 1}, {923, 31}, {1268, 31013}, {1296, 2434}, {1494, 36890}, {1499, 9125}, {1503, 35282}, {1648, 23992}, {1649, 33915}, {1698, 4938}, {1992, 27088}, {2052, 37778}, {2408, 1499}, {2444, 8644}, {2482, 8030}, {2501, 14273}, {2854, 9177}, {3124, 21906}, {3228, 14608}, {3266, 36792}, {3267, 45807}, {3268, 45808}, {3616, 4831}, {3618, 3793}, {3679, 4933}, {3712, 7067}, {4232, 15471}, {4442, 16597}, {4777, 30605}, {4802, 30595}, {5169, 8262}, {5380, 100}, {5466, 523}, {5523, 1560}, {5547, 55}, {5968, 511}, {5969, 45330}, {6091, 3167}, {7181, 1366}, {7316, 56}, {7426, 15303}, {7469, 41606}, {8029, 33919}, {8371, 33921}, {8430, 3569}, {8591, 38239}, {8599, 23287}, {8753, 25}, {8859, 8787}, {8877, 19596}, {9139, 74}, {9154, 98}, {9178, 512}, {9180, 34763}, {9206, 5995}, {9207, 5994}, {9213, 526}, {9214, 30}, {9487, 37860}, {9979, 18311}, {10015, 42760}, {10097, 647}, {10159, 31068}, {10415, 67}, {10416, 11061}, {10422, 1177}, {10557, 14995}, {10558, 39231}, {10561, 2492}, {10562, 39232}, {10630, 111}, {11123, 33906}, {11643, 9716}, {13492, 10354}, {13574, 41498}, {14061, 45291}, {14210, 24038}, {14246, 23}, {14263, 3291}, {14443, 46049}, {14609, 3231}, {14908, 184}, {14977, 525}, {15398, 895}, {15638, 35133}, {15899, 2930}, {16092, 542}, {16741, 16733}, {17948, 543}, {17964, 2502}, {17983, 4}, {17993, 9171}, {18007, 8371}, {18023, 76}, {18818, 598}, {19330, 15141}, {19626, 1501}, {20099, 38304}, {21460, 2080}, {22258, 10417}, {22329, 18800}, {23288, 3906}, {23348, 9181}, {23870, 9204}, {23871, 9205}, {23894, 661}, {23992, 14444}, {25322, 40517}, {25423, 45680}, {30786, 69}, {31125, 141}, {32583, 9145}, {32729, 1576}, {32740, 32}, {33919, 14443}, {34169, 10418}, {34208, 5203}, {34320, 5648}, {34574, 691}, {34760, 9182}, {35179, 2418}, {36060, 48}, {36085, 662}, {36128, 19}, {36142, 163}, {36307, 13}, {36310, 14}, {36792, 23106}, {36821, 3229}, {36827, 1634}, {36877, 16317}, {36894, 441}, {37760, 41595}, {37777, 41616}, {37962, 41618}, {37980, 41612}, {39061, 8591}, {39169, 41615}, {39296, 6082}, {41272, 3051}, {41404, 46276}, {41511, 18876}, {41909, 34161}, {41936, 32740}, {42007, 574}, {42008, 599}, {43448, 24855}, {43926, 3733}, {44146, 34336}, {44182, 41909}, {46111, 264}, {46154, 39}, {46277, 75}

• X₆₇₁ = {X_i,X_j}-harmonic conjugate of X_k for these (i,j,k): {2, 99, 41134}, {2, 115, 9166}, {2, 7620, 11185}, {2, 8591, 2482}, {2, 8596, 8591}, {2, 9166, 14061}, {2, 31125, 42008}, {2, 32480, 574}, {2, 41135, 115}, {2, 42008, 30786}, {5, 8724, 23234}, {6, 10488, 8787}, {6, 11317, 598}, {23, 10415, 10416}, {76, 7841, 7883}, {76, 7911, 32027}, {98, 6321, 10723}, {99, 115, 14061}, {99, 9166, 2}, {111, 148, 16093}, {111, 31125, 30786}, {111, 42008, 2}, {115, 148, 99}, {115, 2482, 5461}, {115, 14931, 7919}, {115, 15300, 14971}, {115, 36523, 41135}, {148, 8591, 8596}, {148, 36523, 9166}, {148, 41135, 2}, {230, 8598, 26613}, {376, 6055, 34473}, {376, 14651, 6055}, {574, 7617, 2}, {620, 14971, 2}, {620, 20094, 99}, {892, 17948, 39061}, {1975, 11318, 7870}, {2482, 5461, 2}, {2482, 8591, 99}, {2549, 7615, 2}, {3734, 14931, 99}, {5077, 40727, 183}, {5254, 8370, 7827}, {5309, 11361, 12150}, {5461, 8596, 99}, {5463, 5469, 5460}, {5464, 5470, 5459}, {5469, 22577, 5463}, {5470, 22578, 5464}, {5523, 37855, 37765}, {6054, 14639, 381}, {6390, 8355, 41133}, {6722, 9167, 2}, {6722, 35369, 99}, {6722, 36521, 9167}, {7610, 35955, 7771}, {7610, 44526, 35955}, {7618, 43620, 2}, {7620, 43448, 2}, {7746, 34504, 33274}, {7825, 20081, 7917}, {7827, 8370, 83}, {7840, 14041, 31173}, {7840, 31173, 7809}, {7841, 7883, 7911}, {7841, 34505, 76}, {7861, 17128, 7944}, {7870, 11318, 7899}, {7924, 9466, 31168}, {8591, 10487, 19911}, {8596, 41135, 5461}, {8787, 10488, 8593}, {8859, 9855, 187}, {9114, 22489, 619}, {9116, 22490, 618}, {9140, 10557, 5466}, {9875, 12258, 9884}, {9882, 19057, 8593}, {9883, 19058, 8593}, {9892, 9894, 7618}, {10054, 10070, 1}, {10630, 11054, 39061}, {10992, 20398, 631}, {11185, 43448, 7790}, {11599, 13178, 7983}, {11648, 18546, 2}, {12188, 22515, 10722}, {12356, 12357, 9884}, {14061, 41134, 2}, {14971, 15300, 620}, {16093, 30786, 99}, {19057, 19058, 6}, {22568, 22570, 9888}, {23234, 23235, 8724}, {24617, 31057, 30856}, {33006, 34511, 7752}, {34505, 44518, 7841}, {35087, 44372, 31998}, {36521, 36523, 41154}, {39103, 39105, 115}

Notes

Let A'B'C' be the 4th Brocard triangle. Let A″ be the pole, wrt the polar circle, of line B'C', and define B″ and C″ cyclically. The lines AA″, BB″, CC″ concur in X₆₇₁. (Randy Hutson, November 30, 2015)

Let A'B'C' be the X₂-Fuhrmann triangle. Let A″ be the reflection of A in B'C', and define B″ and C″ cyclically. A″B″C″ is inversely similar to ABC, with similitude center X₆₇₁. (Randy Hutson, November 30, 2015)

Let P_a be the perspector of the A-Neuberg circle, and define P_b and P_c cyclically. The lines AP_a, BP_b, CP_c concur in X₆₇₁. (Randy Hutson, November 30, 2015)

Let A' be the reflection in BC of the A-vertex of the antipedal triangle of X₂, and define B' and C' cyclically. The circumcircles of A'BC, B'CA, and C'AB concur at X₆₇₁. (Randy Hutson, November 30, 2015)

Let A'B'C' be the 1st Brocard triangle. Let A″ be the reflection of A in line B'C', and define B″ and C″ cyclically. Let A’’’ be the reflection of A' in line BC, and define B’’’ and C’’’ cyclically. Let A* = B″B’’’∩C″C’’’, and define B*and C* cyclically. The lines AA*, BB*, CC* concur in X₆₇₁, which is also X₂-of-A*B*C*. (Randy Hutson, July 11, 2019)