X₁₆₄₉

TRIPOLAR CENTROID OF X₅₂₄

X₁₆₄₉ is the tripolar centroid of X₅₂₄.

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

X₁₆₄₉ (TRIPOLAR CENTROID OF X₅₂₄) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {114, 126}, {2, 523}

• Related Centers: X₁₁₄ (KIEPERT ANTIPODE), X₁₂₆ (-OF-MEDIAL-TRIANGLE), X₂ (CENTROID), X₅₂₃ (ISOGONAL CONJUGATE OF X₁₁₀)

Barycentrics: \((2a^{2} - b^{2} - c^{2})^{2} (b^{2} - c^{2}) : :\)

Search Value (6, 9, 13): \(4.639873061610\)

X₁₆₄₉ lies on the Kiepert parabola.

▸ Incident Central Lines5 lines

{2, 523}, {3, 669}, {39, 647}, {114, 126}, {351, 690}

▸ Functional Relations10 relations

• X₁₆₄₉ = isogonal conjugate of X₃₄₅₇₄

• X₁₆₄₉ = crossdifference of every pair of points on line X₂₃X₁₁₁

• X₁₆₄₉ = X_i-Ceva conjugate of X_j for these (i,j): (2, 1648), (99, 524), (523, 690)

• X₁₆₄₉ = crosspoint of X_i and X_j for these (i,j): (99, 524), (523, 690)

• X₁₆₄₉ = crosssum of X_i and X_j for these (i,j): (110, 691), (111, 512)

• X₁₆₄₉ = perspector of circumconic centered at X₁₆₄₈

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

• X₁₆₄₉ = center of circle {{X₂,X₁₁₀,X₂₇₇₀,X₅₄₆₃,X₅₄₆₄}}

• X₁₆₄₉ = trilinear pole of line X₁₄₄₄₄X_23992

• X₁₆₄₉ = harmonic center of circles {{X₁₃,X₁₅,X₅₄₆₃,X₅₄₆₄}} and {{X₁₄,X₁₆,X₅₄₆₃,X₅₄₆₄}}