X₁₆₄₇

TRIPOLAR CENTROID OF X₅₁₄

X₁₆₄₇ is the tripolar centroid of X₅₁₄.

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

X₁₆₄₇ (TRIPOLAR CENTROID OF X₅₁₄) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {1644, 2}

• Related Centers: X₁₆₄₄ (TRIPOLAR CENTROID OF X₁₉₀), X₂ (CENTROID)

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = bc(b - c)^{2}(2a - b - c)\) (M. Iliev, 5/13/07)

Search Value (6, 9, 13): \(11.473609276314\)

▸ Incident Central Lines4 lines

{1, 2}, {11, 244}, {80, 106}, {149, 1054}

▸ Functional Relations4 relations

• X₁₆₄₇ = reflection of X₁₆₄₄ in X₂

• X₁₆₄₇ = X_i-Ceva conjugate of X_j for these (i,j): (80, 513), (519, 900), (903, 514), (1120, 522)

• X₁₆₄₇ = crosspoint of X_i and X_j for these (i,j): (514, 903), (519, 900)

• X₁₆₄₇ = crosssum of X_i and X_j for these (i,j): (101, 902), (106, 901)