X₁₄₀₀

X₃₇-BETH CONJUGATE OF X₃₇

X₁₄₀₀ = isogonal conjugate of X₃₃₃

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

X₁₄₀₀ (X₃₇-BETH CONJUGATE OF X₃₇) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {2, 7}, {6, 41}

• Related Centers: X₃₇ (CROSSPOINT OF INCENTER AND CENTROID), X₂ (CENTROID), X₇ (GERGONNE POINT), X₆ (SYMMEDIAN POINT), X₄₁ (-CEVA CONJUGATE OF X₃₁)

Trilinears: \((1 - \cos A)(b + c) : :\)

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

Search Value (6, 9, 13): \(0.265457383700\)

▸ Alternate Coordinates1 form

• Trilinears: \(a(\cos B + \cos C) : :\)

▸ Incident Central Lines30 lines

{1, 573}, {2, 7}, {6, 41}, {12, 1213}, {19, 208}, {25, 31}, {36, 572}, {37, 65}, {42, 181}, {44, 583}, {58, 1169}, {85, 1218}, {108, 1172}, {109, 111}, {171, 256}, {213, 1042}, {222, 967}, {292, 694}, {308, 349}, {388, 966}, {478, 603}, {651, 1014}, {910, 1200}, {1100, 1319}, {1122, 1418}, {1171, 1412}, {1254, 1426}, {1258, 1432}, {1333, 1415}, {1420, 1449}

▸ Functional Relations17 relations

• X₁₄₀₀ = isogonal conjugate of X₃₃₃

• X₁₄₀₀ = isotomic conjugate of X₂₈₆₆₀

• X₁₄₀₀ = complement of X₂₀₂₄₅

• X₁₄₀₀ = anticomplement of X₂₁₂₄₆

• X₁₄₀₀ = X_i-Ceva conjugate of X_j for these (i,j): (6, 1409), (56, 1402), (57, 65), (65, 42), (108, 663), (226, 73), (951, 55), (1415, 649), (1427, 1042)

• X₁₄₀₀ = X_i-cross conjugate of X_j for these (i,j): (181, 65), (213, 42), (1402, 1402)

• X₁₄₀₀ = cevapoint of X₂₁₃ and X₁₄₀₂

• X₁₄₀₀ = crosspoint of X_i and X_j for these (i,j): (6, 19), (56, 57), (65, 1427), (225, 226)

• X₁₄₀₀ = crosssum of X_i and X_j for these (i,j): (1, 573), (2, 63), (8, 9), (283, 284)

• X₁₄₀₀ = crossdifference of every pair of points on line X₅₂₂X₆₆₃

• X₁₄₀₀ = X₆₅-Hirst inverse of X₁₂₈₄

• X₁₄₀₀ = bicentric sum of PU(18)

• X₁₄₀₀ = PU(18)-harmonic conjugate of X₆₆₃

• X₁₄₀₀ = barycentric product of PU(81)

• X₁₄₀₀ = trilinear pole of line X₅₁₂X₈₁₀

• X₁₄₀₀ = X₉₂-isoconjugate of X₂₈₃

• X₁₄₀₀ = perspector of ABC and unary cofactor triangle of Gemini triangle 1