X₆₇₆

CROSSDIFFERENCE OF X₃ AND X₁₀₁

X₆₇₆ = crosspoint of X₁₀₅ and X₁₀₈

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

X₆₇₆ (CROSSDIFFERENCE OF X₃ AND X₁₀₁) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {11, 244}, {230, 231}

• Related Centers: X₆₇₇ (TRILINEAR POLE OF LINE X₃X₁₀₁), X₁₁ (FEUERBACH POINT), X₂₄₄ (-LINE CONJUGATE OF X₁₀₀), X₂₃₀ (-CEVA CONJUGATE OF X₁₁₄), X₂₃₁ (-CEVA CONJUGATE OF X₁₂₈)

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = bc(b - c)[b^{3} + c^{3} - 2a^{3} + (b + c)(a^{2} - bc)]\)

Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = af(a,b,c)\)

Search Value (6, 9, 13): \(-2.387896148281\)

▸ Incident Central Lines4 lines

{11, 244}, {105, 659}, {230, 231}, {928, 942}

▸ Functional Relations11 relations

• X₆₇₆ = radical center of the circumcircle, nine-point circle, and incircle (Wilson Stothers, 3/31/2003)

• X₆₇₆ = isogonal conjugate of X₆₇₇

• X₆₇₆ = crosspoint of X₁₀₅ and X₁₀₈

• X₆₇₆ = crosssum of X_i and X_j for these (i,j): (6, 926), (518, 521)

• X₆₇₆ = crossdifference of every pair of points on line X₃X₁₀₁

• X₆₇₆ = circumcenter of X₁₁X₁₀₅X₁₀₈

• X₆₇₆ = intersection of tangents to circumcircle at X₁₀₅ and X₁₀₈, and to nine-point-circle at X₁₁

• X₆₇₆ = pole of line X₂₅X₁₀₅ wrt circumcircle

• X₆₇₆ = perspector of circumconic centered at X₁₅₆₆

• X₆₇₆ = center of circumconic that is locus of trilinear poles of lines passing through X₁₅₆₆

• X₆₇₆ = X₂-Ceva conjugate of X₁₅₆₆