X₂₂₈₇

X₂-ISOCONJUGATE OF X₁₀₄₂

X₂₂₈₇ = isogonal conjugate of X₁₄₂₇

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

X₂₂₈₇ (X₂-ISOCONJUGATE OF X₁₀₄₂) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {2, 6}, {9, 21}

• Related Centers: X₁₄₂₇ (-BETH CONJUGATE OF X₂₂₆), X₂ (CENTROID), X₆ (SYMMEDIAN POINT), X₉ (MITTENPUNKT), X₂₁ (SCHIFFLER 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 X₁₀₄₂

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

Search Value (6, 9, 13): \(4.564594456282\)

▸ Incident Central Lines33 lines

{2, 6}, {8, 29}, {9, 21}, {27, 329}, {28, 72}, {44, 1333}, {58, 936}, {63, 610}, {71, 100}, {145, 2256}, {200, 1253}, {210, 2194}, {213, 2298}, {218, 1010}, {220, 346}, {271, 282}, {274, 1170}, {294, 314}, {307, 651}, {319, 1332}, {332, 949}, {404, 579}, {411, 573}, {644, 2321}, {662, 911}, {758, 1781}, {941, 2271}, {960, 1183}, {997, 1723}, {1014, 1445}, {1098, 1792}, {1761, 2173}, {1809, 2193}

▸ Functional Relations8 relations

• X₂₂₈₇ = isogonal conjugate of X₁₄₂₇

• X₂₂₈₇ = isotomic conjugate of X₁₄₄₆

• X₂₂₈₇ = X_i-Ceva conjugate of X_j for these (i,j): (333, 21), (1098, 2328)

• X₂₂₈₇ = cevapoint of X_i and X_j for these (i,j): (6, 610), (9, 219), (200, 220)

• X₂₂₈₇ = X_i-cross conjugate of X_j for these (i,j): (9, 2322), (200, 1043), (219, 2327), (220, 2328), (2328, 21)

• X₂₂₈₇ = crosspoint of X₃₃₃ and X₁₀₄₃

• X₂₂₈₇ = crosssum of X₁₀₄₂ and X₁₄₀₀

• X₂₂₈₇ = trilinear pole of line X₁₀₂₁X₃₉₀₀