X₂₀₈₆

PK-TRANSFORM OF X₉₉

X₂₀₈₆ = crossdifference of every pair of points on line X₉₉X₅₁₂

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

X₂₀₈₆ (PK-TRANSFORM OF X₉₉) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {2, 6}, {351, 865}

• Related Centers: X₂ (CENTROID), X₆ (SYMMEDIAN POINT), X₃₅₁ (CENTER OF THE PARRY CIRCLE), X₈₆₅ (INTERCEPT OF EULER LINE AND TRILINEAR POLAR OF X)

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = a(b^{2} - c^{2})^{2}(a^{4} - b^{2}c^{2})\)

Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)

Search Value (6, 9, 13): \(-4.538534282519\)

▸ Incident Central Lines3 lines

{2, 6}, {351, 865}, {671, 729}

▸ Functional Relations6 relations

• X₂₀₈₆ = isogonal conjugate of X₃₉₂₉₂

• X₂₀₈₆ = crossdifference of every pair of points on line X₉₉X₅₁₂

• X₂₀₈₆ = X_i-Ceva conjugate of X_j for these (i,j): (98, 669), (694, 512)

• X₂₀₈₆ = crosspoint of X_i and X_j for these {i,j}: {6, 2422}, {512, 694}, {804, 3978}, {1691, 5027}, {2489, 6531}

• X₂₀₈₆ = crosssum of X_i and X_j for these {i,j}: {2, 2396}, {99, 385}, {805, 9468}, {1916, 18829}, {2086, 14824}, {4563, 36212}

• X₂₀₈₆ = trilinear product X_i*X_j for these {i,j}: {115, 1933}, {238, 21823}, {661, 5027}, {740, 21755}, {798, 804}, {1084, 1966}, {1109, 14602}, {1580, 3124}, {1691, 2643}, {1910, 2679}, {1914, 21725}, {1924, 14295}, {1926, 9427}, {1967, 35078}, {2238, 4128}, {3121, 4039}, {3747, 16592}, {3978, 4117}, {4079, 4164}, {4155, 20981}, {7234, 21832}, {18902, 23994}