X₁₉₆₂

BICENTRIC SUM OF PU(32)

X₁₉₆₂ = reflection of X₁₆₃₅ in X₃₅₁

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

X₁₉₆₂ (BICENTRIC SUM OF PU(32)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {1635, 351}

• Related Centers: X₁₆₃₅ (TRIPOLAR CENTROID OF X₁), X₃₅₁ (CENTER OF THE PARRY CIRCLE)

Trilinears: \((b + c)(2a + b + c) : :\)

Search Value (6, 9, 13): \(1.882074504097\)

▸ Incident Central Lines6 lines

{1, 21}, {2, 740}, {37, 42}, {55, 199}, {100, 1255}, {351, 1635}

▸ Functional Relations13 relations

• X₁₉₆₂ = reflection of X₁₆₃₅ in X₃₅₁

• X₁₉₆₂ = isogonal conjugate of isotomic conjugate of X₄₆₄₇

• X₁₉₆₂ = crossdifference of every pair of points on line X₆₆₁X₁₀₁₉

• X₁₉₆₂ = homothetic center of incentral triangle and n(Medial)*n(Incentral) triangle

• X₁₉₆₂ = X₂-of-n(Medial)*n(Incentral)-triangle

• X₁₉₆₂ = X_i-Ceva conjugate of X_j for these (i,j): (1, 1100), (100, 661), (1125, 1213)

• X₁₉₆₂ = crosspoint of X_i and X_j for these (i,j): (1, 37), (1100, 1125)

• X₁₉₆₂ = crosssum of X_i and X_j for these (i,j): (1, 81), (1126, 1255)

• X₁₉₆₂ = X₂-of incentral triangle

• X₁₉₆₂ = bicentric sum of PU(32)

• X₁₉₆₂ = PU(32)-harmonic conjugate of X₆₆₁

• X₁₉₆₂ = complement of X₁₇₁₆₃

• X₁₉₆₂ = homothetic center of Gemini triangle 17 and cross-triangle of Gemini triangles 15 and 17