X₉₆₀

INTERSECTION OF LINES X₁X_6 AND X₅X_10

X₉₆₀ = midpoint of X₁ and X₇₂

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

X₉₆₀ (INTERSECTION OF LINES X₁X_6 AND X₅X_10) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {1, 72}

• Related Centers: X₁ (INCENTER), X₇₂ (ISOGONAL CONJUGATE OF X₂₈)

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = (b + c - a)(b^{2} + c^{2} + ab + ac)\)

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): \(3.679190031981\)

▸ Incident Central Lines20 lines

{1, 6}, {2, 65}, {3, 997}, {5, 10}, {8, 210}, {12, 908}, {19, 965}, {21, 60}, {36, 191}, {40, 936}, {46, 474}, {55, 78}, {56, 63}, {113, 123}, {221, 1038}, {241, 1042}, {329, 388}, {758, 942}, {912, 993}, {978, 986}

▸ Functional Relations18 relations

• X₉₆₀ = midpoint of X₁ and X₇₂

• X₉₆₀ = reflection of X₉₄₂ in X₁₁₂₅

• X₉₆₀ = isogonal conjugate of X₉₆₁

• X₉₆₀ = isotomic conjugate of X₃₁₆₄₃

• X₉₆₀ = complement of X₆₅

• X₉₆₀ = anticomplementary conjugate of X₄₄₂

• X₉₆₀ = crosspoint of X_i and X_j for these (i,j): (2, 314), (8, 21)

• X₉₆₀ = crosssum of X_i and X_j for these (i,j): (6, 1402), (56, 65)

• X₉₆₀ = anticomplement of X₃₈₁₂

• X₉₆₀ = {X₁,X₉}-harmonic conjugate of X₉₅₈

• X₉₆₀ = perspector of circumconic centered at X₂₀₉₂

• X₉₆₀ = center of circumconic that is locus of trilinear poles of lines passing through X₂₀₉₂

• X₉₆₀ = X₂-Ceva conjugate of X₂₀₉₂

• X₉₆₀ = X₁₁-of-X₁-Brocard-triangle

• X₉₆₀ = X₃₀₃₅-of-inner-Garcia-triangle

• X₉₆₀ = X₁₂₂₄₁-of-excentral-triangle

• X₉₆₀ = polar conjugate of isogonal conjugate of X₂₂₀₇₄

• X₉₆₀ = excentral-to-ABC barycentric image of X₁₀