X₂₂₉₃

X₂-ISOCONJUGATE OF X₁₁₇₀

X₂₂₉₃ = crossdifference of every pair of points on line X₅₁₄X₆₅₇

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

X₂₂₉₃ (X₂-ISOCONJUGATE OF X₁₁₇₀) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {1, 7}, {6, 31}

• Related Centers: X₁ (INCENTER), X₇ (GERGONNE POINT), X₆ (SYMMEDIAN POINT), X₃₁ (2nd POWER POINT)

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

Barycentrics: \(a^{2}/f(a,b,c) : b^{2}/f(b,c,a): c^{2}/f(c,a,b)\)

Search Value (6, 9, 13): \(2.306531683107\)

▸ Alternate Coordinates1 form

• Trilinears: \(\sec^{2}(B/2) + \sec^{2}(C/2) : :\) (Randy Hutson, 9/23/2011)

▸ Incident Central Lines19 lines

{1, 7}, {3, 1471}, {6, 31}, {9, 2340}, {33, 1839}, {37, 2310}, {48, 1486}, {73, 1456}, {200, 391}, {284, 2195}, {354, 1418}, {500, 1066}, {608, 2356}, {651, 2346}, {692, 2317}, {756, 1864}, {1001, 1818}, {1201, 1279}, {1400, 2223}

▸ Functional Relations10 relations

• X₂₂₉₃ = X_i-Ceva conjugate of X_j for these (i,j): (1, 354), (354, 1475), (651, 657), (1292, 649)

• X₂₂₉₃ = crosspoint of X_i and X_j for these (i,j): (1, 55), (6, 2191), (354, 1212)

• X₂₂₉₃ = crosssum of X_i and X_j for these (i,j): (1, 7), (1170, 2346)

• X₂₂₉₃ = {X₁,X₁₇₄₂}-harmonic Conjugate of X₇

• X₂₂₉₃ = crossdifference of every pair of points on line X₅₁₄X₆₅₇

• X₂₂₉₃ = bicentric sum of PU(104)

• X₂₂₉₃ = PU(104)-harmonic conjugate of X₆₅₇

• X₂₂₉₃ = isogonal conjugate of [intersection of tangents at X₁ and X₇ to hyperbola passing through X₁, X₇ and the excenters]

• X₂₂₉₃ = isogonal conjugate of [crosspoint of X₁ and X₇ wrt the excentral triangle]

• X₂₂₉₃ = perspector of ABC and unary cofactor triangle of Honsberger triangle