X₁₉₄₈

CROSSDIFFERENCE OF PU(19)

X₁₉₄₈ = X₁₉₅₂-Ceva conjugate of X₁₉₄₇

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

X₁₉₄₈ (CROSSDIFFERENCE OF PU(19)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {2, 92}, {9, 264}

• Related Centers: X₂ (CENTROID), X₉₂ (CEVAPOINT OF INCENTER AND CLAWSON POINT), X₉ (MITTENPUNKT), X₂₆₄ (ISOTOMIC CONJUGATE OF CIRCUMCENTER)

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = (\cos^{2} A - \cos B \cos C) \csc 2A\)

Barycentrics: \(b c (a - b - c) (a^{4} - a^{2} (b^{2} - b c + c^{2}) - b c (b - c)^{2})/(a^{2} - b^{2} - c^{2}) : :\)

Search Value (6, 9, 13): \(2.834102922843\)

▸ Incident Central Lines3 lines

{2, 92}, {9, 264}, {24, 547}

▸ Functional Relations8 relations

• X₁₉₄₈ = isogonal conjugate of X₁₉₄₉

• X₁₉₄₈ = X₂-Ceva conjugate of X₃₉₀₃₆

• X₁₉₄₈ = X₁₉₅₂-Ceva conjugate of X₁₉₄₇

• X₁₉₄₈ = crosssum of X₁₉₅₀ and X₁₉₅₁

• X₁₉₄₈ = perspector of conic {A, B, C,PU(20)}

• X₁₉₄₈ = intersection of trilinear polars of P(20) and U(20)

• X₁₉₄₈ = pole wrt polar circle of line X₆₅X₆₅₀, PU(15))

• X₁₉₄₈ = X₄₈-isoconjugate (polar conjugate) of X₁₉₃₇