X₂₂₃₈

X₂-ISOCONJUGATE OF X₇₄₁

X₂₂₃₈ = bicentric sum of PU(90)

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

X₂₂₃₈ (X₂-ISOCONJUGATE OF X₇₄₁) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {2, 6}, {9, 43}

• Related Centers: X₂ (CENTROID), X₆ (SYMMEDIAN POINT), X₉ (MITTENPUNKT), X₄₃ (-CEVA CONJUGATE OF X₁)

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

Search Value (6, 9, 13): \(-6.887116886156\)

▸ Alternate Coordinates1 form

• Trilinears: \((\sin A + \sin B + \sin C) \csc A - (\csc A + \csc B + \csc C) \sin A : :\)

▸ Incident Central Lines23 lines

{1, 1573}, {2, 6}, {8, 2176}, {9, 43}, {10, 213}, {32, 1009}, {37, 42}, {44, 513}, {218, 442}, {220, 1834}, {238, 1914}, {239, 350}, {291, 1757}, {294, 857}, {405, 2271}, {429, 607}, {748, 2280}, {800, 1713}, {860, 1783}, {862, 2201}, {978, 2275}, {1107, 1193}, {1778, 2305}

▸ Functional Relations10 relations

• X₂₂₃₈ = isogonal conjugate of X₃₇₁₂₈

• X₂₂₃₈ = complement of X₃₀₉₄₁

• X₂₂₃₈ = cevapoint of X_i and X_j for these {i,j}: {6, 9509}, {1757, 2664}, {20683, 21830}

• X₂₂₃₈ = crosssum of X_i and X_j for these {i,j}: {1, 2238}, {6, 3286}, {9, 35104}, {81, 1931}, {86, 2669}, {291, 292}, {659, 1015}, {741, 2311}, {17103, 33295}

• X₂₂₃₈ = trilinear pole of line X₄₀₉₄X_4155

• X₂₂₃₈ = X_i-Ceva conjugate conjugate of X_j for these (i,j): (98, 55), (660, 512), (666, 523), (1929, 1962), (2665, 2667)

• X₂₂₃₈ = crosspoint of X_i and X_j for these (i,j): (1, 37128), (2, 13576), (37, 9278), (42, 2107), (57, 35108), (238, 239), (660, 1016). (740, 16609)

• X₂₂₃₈ = bicentric sum of PU(90)

• X₂₂₃₈ = PU(90)-harmonic conjugate of X₄₃₆₇

• X₂₂₃₈ = {X₁₀,X₂₁₃}-harmonic conjugate of X₂₂₉₅