X₁₆₃₅

TRIPOLAR CENTROID OF X₁

X₁₆₃₅ is the tripolar centroid of X₁.

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

X₁₆₃₅ (TRIPOLAR CENTROID OF X₁) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {1962, 351}

• Related Centers: X₁₉₆₂ (BICENTRIC SUM OF PU(32)), X₃₅₁ (CENTER OF THE PARRY CIRCLE)

Trilinears: \((b - c)(b + c - 2a) : :\) (M. Iliev, 5/13/07)

Search Value (6, 9, 13): \(-7.512482264253\)

▸ Incident Central Lines7 lines

{2, 812}, {44, 513}, {88, 1022}, {100, 101}, {105, 1024}, {244, 665}, {900, 1644}

▸ Functional Relations14 relations

• X₁₆₃₅ = reflection of X₁₉₆₂ in X₃₅₁

• X₁₆₃₅ = isogonal conjugate of X₃₂₅₇

• X₁₆₃₅ = complement of X₂₁₂₉₇

• X₁₆₃₅ = anticomplement of X₄₉₂₈

• X₁₆₃₅ = X_i-Ceva conjugate of X_j for these (i,j): (2, 38979), (44, 2087), (88, 244), (104, 2310), (662, 214), (1022, 513), (1023, 44), (2161, 2170)

• X₁₆₃₅ = X₂₀₈₇-cross conjugate of X₄₄

• X₁₆₃₅ = crosspoint of X_i and X_j for these (i,j): (44, 1023), (57, 2222), (88, 100), (101, 909), (190, 1120), (513, 1022), (662, 759)

• X₁₆₃₅ = crosssum of X_i and X_j for these (i,j): (1, 1635), (44, 513), (88, 1022), (100, 1023), (514, 908), (649, 1149), (661, 758)

• X₁₆₃₅ = bicentric sum of PU(34)

• X₁₆₃₅ = perspector of hyperbola {{A, B, C,X₁,X₄₄}}

• X₁₆₃₅ = PU(34)-harmonic conjugate of X₂₄₄

• X₁₆₃₅ = trilinear pole of line X₂₀₈₇X₃₂₅₁

• X₁₆₃₅ = centroid of antiorthic axis intercepts with sidelines of ABC

• X₁₆₃₅ = X₆₄₇-of-2nd-extouch-triangle