X₂₃₀₀

X₂-ISOCONJUGATE OF X₁₂₂₀

X₂₃₀₀ = perspector of unary cofactor triangles of Gemini triangles 39 and 40

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

X₂₃₀₀ (X₂-ISOCONJUGATE OF X₁₂₂₀) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {1, 6}, {32, 48}

• Related Centers: X₁ (INCENTER), X₆ (SYMMEDIAN POINT), X₃₂ (3rd POWER POINT), X₄₈ (CROSSPOINT OF X₁ AND X₆₃)

Trilinears: \(a/f(a,b,c) : b/f(b,c,a) : c/f(c,a,b)\), where f(a,b,c) is as in X₁₂₂₀

Barycentrics: \(a^{2}/f(a,b,c) : b^{2}/f(b,c,a): c^{2}/f(c,a,b)\)

Search Value (6, 9, 13): \(0.624581062315\)

▸ Alternate Coordinates1 form

• Trilinears: \(a^{2}(as + S_{A}) : b^{2}(bs + S_{B}) : c^{2}(cs + S_{C}) (César Lozada, 9/07/2013)\)

▸ Incident Central Lines23 lines

{1, 6}, {10, 992}, {19, 1572}, {31, 184}, {32, 48}, {36, 2305}, {39, 71}, {81, 261}, {110, 1169}, {239, 314}, {284, 893}, {394, 2221}, {572, 595}, {573, 995}, {579, 2275}, {849, 1333}, {869, 2209}, {1015, 2260}, {1185, 2280}, {1193, 1682}, {1201, 1400}, {1918, 1964}, {2174, 2220}

▸ Functional Relations7 relations

• X₂₃₀₀ = X_i-Ceva conjugate of X_j for these (i,j): (6, 2092), (110, 667)

• X₂₃₀₀ = crosspoint of X_i and X_j for these (i,j): (6, 1333), (31, 904), (56, 81)

• X₂₃₀₀ = crosssum of X_i and X_j for these (i,j): (2, 321), (8, 37), (75, 1909), (1791, 2298)

• X₂₃₀₀ = isogonal conjugate of X₃₀₇₁₀

• X₂₃₀₀ = polar conjugate of isotomic conjugate of X₂₂₃₄₅

• X₂₃₀₀ = perspector of unary cofactor triangles of Gemini triangles 39 and 40

• X₂₃₀₀ = crossdifference of every pair of points on line X₅₁₃X₂₅₁₇ (the perspectrix of Gemini triangles 39 and 40)