X₁₆₄₈

TRIPOLAR CENTROID OF X₅₂₃

X₁₆₄₈ is the tripolar centroid of X₅₂₃.

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

X₁₆₄₈ (TRIPOLAR CENTROID OF X₅₂₃) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {1641, 2}

• Related Centers: X₁₆₄₁ (TRIPOLAR CENTROID OF X₉₉), X₂ (CENTROID)

Trilinears: \(bc(b^{2} - c^{2})^{2}(b^{2} + c^{2} - 2a^{2}) : :\)

Search Value (6, 9, 13): \(6.428022286341\)

▸ Incident Central Lines3 lines

{2, 6}, {115, 125}, {669, 865}

▸ Functional Relations16 relations

• X₁₆₄₈ = reflection of X₁₆₄₁ in X₂

• X₁₆₄₈ = isotomic conjugate of isogonal conjugate of X₂₁₉₀₆

• X₁₆₄₈ = X_i-Ceva conjugate of X_j for these (i,j): (2, 1649), (67, 512), (468, 351), (524, 690), (671, 523)

• X₁₆₄₈ = crosspoint of X_i and X_j for these (i,j): (523, 671), (524, 690)

• X₁₆₄₈ = crosssum of X_i and X_j for these (i,j): (110, 187), (111, 691)

• X₁₆₄₈ = intersection of tangents to Hutson-Parry circle at X₁₃ and X₁₄

• X₁₆₄₈ = pole wrt Hutson-Parry circle of Fermat axis

• X₁₆₄₈ = inverse-in-Hutson-Parry-circle of X₁₁₅

• X₁₆₄₈ = perspector of circumconic centered at X₁₆₄₉

• X₁₆₄₈ = center of circumconic that is locus of trilinear poles of lines passing through X₁₆₄₉

• X₁₆₄₈ = intersection of line PU(40) (X₁₁₅X₁₂₅) and trilinear polar of cevapoint of PU(40)

• X₁₆₄₈ = X₂₅₀₂-of-4th-Brocard-triangle

• X₁₆₄₈ = X₂₅₀₂-of-orthocentroidal-triangle

• X₁₆₄₈ = centroid of (degenerate) cross-triangle of 4th Brocard and orthocentroidal triangle

• X₁₆₄₈ = trilinear pole of line X₂₆₈₂X₁₄₄₄₃

• X₁₆₄₈ = {X₁₃₆₃₆,X₁₃₇₂₂}-harmonic conjugate of X₁₁₅