X₁₆₄₀

TRIPOLAR CENTROID OF X₉₈

X₁₆₄₀ is the tripolar centroid of X₉₈.

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

X₁₆₄₀ (TRIPOLAR CENTROID OF X₉₈) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {115, 125}, {2, 525}

• Related Centers: X₁₁₅ (CENTER OF KIEPERT HYPERBOLA), X₁₂₅ (CENTER OF JERABEK HYPERBOLA), X₂ (CENTROID), X₅₂₅ (ISOGONAL CONJUGATE OF X₁₁₂)

Trilinears: \(bc(b^{2} - c^{2})(2a^{6} - b^{6} - c^{6} - 2a^{4}b^{2} - 2a^{4}c^{2} + a^{2}b^{4} + a^{2}c^{4} + b^{4}c^{2} + b^{2}c^{4}) : :\) (M. Iliev, 5/25/07)

Search Value (6, 9, 13): \(-1.883721210225\)

▸ Incident Central Lines6 lines

{2, 525}, {4, 1499}, {6, 523}, {39, 647}, {51, 512}, {115, 125}

▸ Functional Relations7 relations

• X₁₆₄₀ = radical center of Brocard circle, orthocentroidal circle, and orthosymmedial circle

• X₁₆₄₀ = radical center of orthocentroidal circle, orthosymmedial circle, and circle O(2,6)

• X₁₆₄₀ = X₃₂₆₈-of-1st-Brocard-triangle

• X₁₆₄₀ = orthocenter of X₂X₄X₆

• X₁₆₄₀ = orthoptic-circle-of-Steiner-inellipse-inverse of X₃₄₃₆₆

• X₁₆₄₀ = inverse-in-Hutson-Parry-circle of X₁₆₃₇

• X₁₆₄₀ = {X₁₃₆₃₆,X₁₃₇₂₂}-harmonic conjugate of X₁₆₃₇