X₁₉₄₄

CROSSDIFFERENCE OF PU(18)

X₁₉₄₄ = perspector of conic {{A, B, C,X₃₃₃,X₆₆₄}}

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

X₁₉₄₄ (CROSSDIFFERENCE OF PU(18)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {2, 7}, {75, 219}

• Related Centers: X₁₉₄₅ (TRILINEAR POLE OF PU(18)), X₂ (CENTROID), X₇ (GERGONNE POINT), X₇₅ (ISOTOMIC CONJUGATE OF INCENTER), X₂₁₉ (-CEVA CONJUGATE OF X₅₅)

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

Barycentrics: \(\cos^{2} A - \cos B \cos C : \cos^{2} B - \cos C \cos A : \cos^{2} C - \cos A \cos B\)

Search Value (6, 9, 13): \(5.353891257589\)

▸ Incident Central Lines21 lines

{2, 7}, {69, 281}, {75, 219}, {92, 394}, {220, 4363}, {239, 2323}, {242, 511}, {314, 1172}, {448, 662}, {522, 663}, {524, 1146}, {534, 5195}, {666, 1814}, {960, 1010}, {990, 997}, {1212, 4670}, {1332, 3262}, {1737, 1757}, {1958, 2289}, {2324, 3729}, {2607, 3792}

▸ Functional Relations8 relations

• X₁₉₄₄ = isogonal conjugate of X₁₉₄₅

• X₁₉₄₄ = isotomic conjugate of X₁₉₅₂

• X₁₉₄₄ = X_i-complementary conjugate of X_j for these (i,j): (2648, 141), (2701, 4885)

• X₁₉₄₄ = X_i-cross conjugate of X_j for these (i,j): (1936, 5088), (1951, 243)

• X₁₉₄₄ = X₂-Ceva conjugate of X₃₉₀₃₅

• X₁₉₄₄ = perspector of conic {{A, B, C,X₃₃₃,X₆₆₄}}

• X₁₉₄₄ = X_i-isoconjugate of X_j for these (i,j): (1, 1945), (4, 1949), (6, 1937), (19, 296), (31, 1952), (65, 2249)

• X₁₉₄₄ = {X_i,X_j}-harmonic conjugate of X_k for these (i,j,k): (92, 394, 1943), (2323, 4858, 239)