X₃₁₈₅

X₂₁-CEVA CONJUGATE OF X₆

X₃₁₈₅ = isogonal conjugate of X₂₉₉₅

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

X₃₁₈₅ (X₂₁-CEVA CONJUGATE OF X₆) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Related Centers: X₂₁ (SCHIFFLER POINT), X₆ (SYMMEDIAN POINT)

Trilinears: \(u(-u/x + v/y + w/z) : v(u/x - v/y + w/z) : w(u/x + v/y - w/z)\), where \(x : y : z\) = X₂₁ and \(u : v : w\) = X₆

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): \(-25.504943904034\)

▸ Alternate Coordinates1 form

• Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = a^{3}[a^{2}b + a^{2}c - abc - b^{3} - c^{3}] (E\). Danneels), X₃₁₈₅ lies on these lines: 1,859 3,960 12,1894 19,25 21,1610 31,48 35,2933 47,1437 100,312 184,2361 212,692 227,1875 674,3190 851,1836 1011,2182 1460,2178 1630,2328 1953,1962 2176,2223 2179,2304 2308,2317

▸ Functional Relations5 relations

• X₃₁₈₅ = isogonal conjugate of X₂₉₉₅

• X₃₁₈₅ = X₂₁-Ceva conjugate of X₆

• X₃₁₈₅ = crosspoint of X₁₀₀ and X₂₁₄₉

• X₃₁₈₅ = crosssum of X₁₂₃ and X₅₂₅

• X₃₁₈₅ = crossdifference of every pair of points on the line X₉₀₅X₁₅₇₇