X₃₁₆₀

X₂-CEVA CONJUGATE OF X₇

X₃₁₆₀ = perspector of triangle ABC and the tangential triangle of the conic that passes through A, B, C and has center X₇

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

X₃₁₆₀ (X₂-CEVA CONJUGATE OF X₇) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {175, 176}

• Related Centers: X₁₇₅ (ISOPERIMETRIC POINT), X₁₇₆ (EQUAL DETOUR POINT)

Trilinears: \(u(-u/x + v/y + w/z) : v(u/x - v/y + w/z) : w(u/x + v/y - w/z)\), where \(x : y : z\) = X₂ and \(u : v : w\) = X₇

Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\), where \(f(a,b,c) = u(-u/x + v/y + w/z)\)

Search Value (6, 9, 13): \(-2.980567436125\)

▸ Incident Central Lines10 lines

{1, 7}, {3, 934}, {8, 348}, {9, 2124}, {144, 1419}, {220, 651}, {241, 2275}, {738, 1697}, {944, 1565}, {1358, 1388}

▸ Functional Relations9 relations

• X₃₁₆₀ = perspector of triangle ABC and the tangential triangle of the conic that passes through A, B, C and has center X₇

• X₃₁₆₀ = midpoint of X₁₇₅ and X₁₇₆

• X₃₁₆₀ = X₂-Ceva conjugate of X₇

• X₃₁₆₀ = cevapoint of X_i and X_j for these (i,j): (1, 2124),(165, 1419)

• X₃₁₆₀ = X₁₆₅-cross conjugate of X₁₄₄

• X₃₁₆₀ = crosspoint of X₂ and X₁₄₄

• X₃₁₆₀ = crosssum of X₆₆₃ and X₃₀₂₂

• X₃₁₆₀ = X₉₉-beth conjugate of X₈

• X₃₁₆₀ = center of circumconic that is locus of trilinear poles of lines passing through X₇