X₂₂₂₄

X₂-ISOCONJUGATE OF X₆₇₄

X₂₂₂₄ = cevapoint of X(55,2110)

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

X₂₂₂₄ (X₂-ISOCONJUGATE OF X₆₇₄) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {2, 101}, {81, 163}

• Related Centers: X₂ (CENTROID), X₁₀₁ (Ψ(INCENTER, SYMMEDIAN POINT)), X₈₁ (CEVAPOINT OF INCENTER AND SYMMEDIAN POINT), X₁₆₃ (TRILINEAR PRODUCT X₆*X₁₁₀)

Trilinears: \(a/f(a,b,c) : b/f(b,c,a) : c/f(c,a,b)\), where f(a,b,c) is as in X₆₇₄

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

Search Value (6, 9, 13): \(-13.187294687595\)

▸ Incident Central Lines8 lines

{1, 692}, {2, 101}, {36, 291}, {57, 609}, {81, 163}, {274, 662}, {279, 1461}, {1429, 2006}

▸ Functional Relations5 relations

• X₂₂₂₄ = X_i-Ceva conjugate of X_j for these (i,j): (911, 41), (1037, 1362)

• X₂₂₂₄ = cevapoint of X(55,2110)

• X₂₂₂₄ = crosspoint of X_i and X_j for these (i,j): (6, 105), (31, 1911), (59, 919), (672, 1458)

• X₂₂₂₄ = crosssum of X_i and X_j for these (i,j): (2, 518), (11, 918), (75, 350), (105, 1814)

• X₂₂₂₄ = eigencenter of Gemini triangle 7