X₁₉₅₅

CROSSDIFFERENCE OF PU(21)

X₁₉₅₅ = isogonal conjugate of X₁₉₅₆

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

X₁₉₅₅ (CROSSDIFFERENCE OF PU(21)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {1, 19}, {58, 1047}

• Related Centers: X₁₉₅₆ (TRILINEAR POLE OF PU(21)), X₁ (INCENTER), X₁₉ (CLAWSON POINT), X₅₈ (ISOGONAL CONJUGATE OF X₁₀), X₁₀₄₇ (-CEVA CONJUGATE OF X₁)

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

Search Value (6, 9, 13): \(2.909833394820\)

▸ Alternate Coordinates1 form

• Trilinears: \(a^{4} (a^{2} - b^{2} - c^{2})^{2} - b^{2} c^{2} (b^{2} - c^{2} - a^{2}) (c^{2} - a^{2} - b^{2}) : :\)

▸ Incident Central Lines6 lines

{1, 19}, {47, 1740}, {58, 1047}, {92, 1954}, {293, 1755}, {1580, 1733}

▸ Functional Relations4 relations

• X₁₉₅₅ = isogonal conjugate of X₁₉₅₆

• X₁₉₅₅ = X_i-Ceva conjugate of X_j for these (i,j): (2, 39038), (293, 1), (1755, 1580)

• X₁₉₅₅ = X_i-aleph conjugate of X_j for these (i,j): (98, 1733), (293, 1955)

• X₁₉₅₅ = perspector of hyperbola {{A, B, C,X₁₆₂,X₂₁₆₇}}