X₃₀₅₆

INTERSECTION OF LINES X₁X_256 AND X₆X_31

X₃₀₅₆ = reflection of X₁₄₆₉ in X₁

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

X₃₀₅₆ (INTERSECTION OF LINES X₁X_256 AND X₆X_31) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {1469, 1}

• Related Centers: X₁₄₆₉ (-BETH CONJUGATE OF X₉₈₄), X₁ (INCENTER)

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

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

Search Value (6, 9, 13): \(3.009842275641\)

▸ Incident Central Lines15 lines

{1, 256}, {3, 613}, {6, 31}, {11, 141}, {33, 1843}, {35, 182}, {37, 263}, {51, 612}, {56, 1350}, {69, 350}, {87, 291}, {144, 145}, {210, 391}, {573, 2223}, {611, 1351}

▸ Functional Relations6 relations

• X₃₀₅₆ = reflection of X₁₄₆₉ in X₁

• X₃₀₅₆ = isogonal conjugate of isotomic conjugate of X₃₇₀₅

• X₃₀₅₆ = crosspoint of X_i and X_j for these (i,j): (1, 2319), (284, 314), (982, 3061)

• X₃₀₅₆ = crosssum of X_i and X_j for these (i,j): (1, 1423), (226, 1402)

• X₃₀₅₆ = X₆-of-Mandart-incircle-triangle

• X₃₀₅₆ = homothetic center of intangents triangle and reflection of extangents triangle in X₆