X₂₁₈₂

X₂-ISOCONJUGATE OF X₁₀₂

X₂₁₈₂ = crossdifference of every pair of points on line X₁X₅₂₁

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

X₂₁₈₂ (X₂-ISOCONJUGATE OF X₁₀₂) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {3, 9}, {6, 19}

• Related Centers: X₃ (CIRCUMCENTER), X₉ (MITTENPUNKT), X₆ (SYMMEDIAN POINT), X₁₉ (CLAWSON POINT)

Trilinears: \(a/f(a,b,c) : b/f(b,c,a) : c/f(c,a,b)\), where f(a,b,c) is as in X₁₀₂

Search Value (6, 9, 13): \(-3.455657938362\)

▸ Alternate Coordinates2 forms

• Trilinears: \(a[(b + c)\sec A - b \sec B - c \sec C] : :\)

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

▸ Incident Central Lines25 lines

{3, 9}, {6, 19}, {25, 1864}, {33, 154}, {37, 48}, {44, 513}, {46, 1743}, {51, 2355}, {169, 374}, {184, 1824}, {197, 210}, {219, 1766}, {407, 1901}, {517, 2323}, {572, 1630}, {578, 1871}, {604, 1108}, {909, 1319}, {960, 1610}, {1100, 1953}, {1212, 2267}, {1214, 1726}, {1404, 2170}, {1498, 1753}, {1503, 1861}

▸ Functional Relations8 relations

• X₂₁₈₂ = isogonal conjugate of X₃₆₁₀₀

• X₂₁₈₂ = X_i-Ceva conjugate of X_j for these (i,j): (1295, 55), (1465, 1319)

• X₂₁₈₂ = crosspoint of X_i and X_j for these (i,j): (4, 2006, 57, 104)

• X₂₁₈₂ = crosssum of X_i and X_j for these (i,j): (1, 2182), (3, 2323), (9, 517)

• X₂₁₈₂ = {X₆,X₁₉}-harmonic conjugate of X₂₂₆₂

• X₂₁₈₂ = crossdifference of every pair of points on line X₁X₅₂₁

• X₂₁₈₂ = bicentric sum of PU(100)

• X₂₁₈₂ = PU(100)-harmonic conjugate of X₆₁₂₉