X₂₃₂₇

X₂-ISOCONJUGATE OF (1426)

X₂₃₂₇ = crosspoint of X₁₇₉₂ and X₁₈₁₂

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

X₂₃₂₇ (X₂-ISOCONJUGATE OF (1426)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {9, 21}, {48, 63}

• Related Centers: X₉ (MITTENPUNKT), X₂₁ (SCHIFFLER POINT), X₄₈ (CROSSPOINT OF X₁ AND X₆₃), X₆₃ (ISOGONAL CONJUGATE OF X₁₉)

Trilinears: \(a/f(a,b,c) : b/f(b,c,a) : c/f(c,a,b)\), where f(a,b,c) is as in X₁₄₂₆

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

Search Value (6, 9, 13): \(5.045020139329\)

▸ Incident Central Lines12 lines

{9, 21}, {27, 908}, {48, 63}, {219, 283}, {306, 319}, {394, 1073}, {758, 1744}, {1043, 2322}, {1333, 1801}, {1789, 1800}, {1792, 1802}, {2200, 2359}

▸ Functional Relations5 relations

• X₂₃₂₇ = X_i-Ceva conjugate of X_j for these (i,j): (1043, 2328), (1812, 283)

• X₂₃₂₇ = cevapoint of X_i and X_j for these (i,j): (219, 2289), (1260, 1802)

• X₂₃₂₇ = X_i-cross conjugate of X_j for these (i,j): (219, 2287), (1260, 1792)

• X₂₃₂₇ = crosspoint of X₁₇₉₂ and X₁₈₁₂

• X₂₃₂₇ = crosssum of X₁₄₂₆ and X₁₈₈₀