X₂₆₄₃

DIFFERENCE OF PU(79)

X₂₆₄₃ = trilinear pole wrt incentral triangle of line X₁X₂₁

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

X₂₆₄₃ (DIFFERENCE OF PU(79)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {19, 560}, {1, 662}

• Related Centers: X₁₉ (CLAWSON POINT), X₅₆₀ (4th POWER POINT), X₁ (INCENTER), X₆₆₂ (TRILINEAR POLE OF LINE X₁X₂₁)

Trilinears: \(1/(\cot C - \cot A) - 1/(\cot B - \cot A) : :\)

Search Value (6, 9, 13): \(1.579865402485\)

▸ Alternate Coordinates4 forms

• Trilinears: \((b^{2} - c^{2})^{2}\) (M. Iliev, 5/13/07)

• Trilinears: \((\cot B - \cot C)^{2} : :\)

• Trilinears: \((\cos 2B - \cos 2C)^{2} : :\)

• Trilinears: (distance from A to line X₂X₆)² : :

X₂₆₄₃ lies on the incentral inellipse (i.e., Hofstadter ellipse E(1/2)).

▸ Incident Central Lines18 lines

{1, 662}, {19, 560}, {31, 2153}, {37, 2054}, {65, 2652}, {75, 1581}, {244, 2611}, {267, 849}, {523, 1086}, {678, 1962}, {872, 2171}, {922, 2173}, {1098, 1247}, {1109, 2632}, {1580, 2244}, {1953, 1964}, {1959, 2234}, {1931, 2641}

▸ Functional Relations8 relations

• X₂₆₄₃ = reflection of X₄₀₉₄ in X₃₇

• X₂₆₄₃ = complement of X₂₁₂₉₅

• X₂₆₄₃ = trilinear pole wrt incentral triangle of line X₁X₂₁

• X₂₆₄₃ = incentral isotomic conjugate of X₅₁₂

• X₂₆₄₃ = crossdifference of every pair of points on line X₁₆₃X₆₆₂

• X₂₆₄₃ = antipode in the incentral inellipse of X₄₀₉₄

• X₂₆₄₃ = trilinear square of X₆₆₁

• X₂₆₄₃ = PU(79)-harmonic conjugate of X₂₆₄₂