X₂₁₆₁

X₂-ISOCONJUGATE OF X₃₆

X₂₁₆₁ = trilinear pole of line X₄₂X₆₆₃

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

X₂₁₆₁ (X₂-ISOCONJUGATE OF X₃₆) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {19, 53}, {9, 80}

• Related Centers: X₂₀₀₆ (ORTHOCORRESPONDENT OF X₈₀), X₁₄₁₁ (-BETH CONJUGATE OF X₈₀), X₁₉ (CLAWSON POINT), X₅₃ (SYMMEDIAN POINT OF ORTHIC TRIANGLE), X₉ (MITTENPUNKT), X₈₀ (REFLECTION OF INCENTER IN FEUERBACH POINT)

Trilinears: \(a/f(a,b,c) : b/f(b,c,a) : c/f(c,a,b)\), where f(a,b,c) is as in X₃₆

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

Search Value (6, 9, 13): \(3.617834705260\)

▸ Alternate Coordinates1 form

• Trilinears: \(g(A,B,C) : g(B,C,A) : g(C,A,B)\), where \(g(A, B, C) = (\sin A)/(1 - 2 \cos A)\)

▸ Incident Central Lines22 lines

{1, 2364}, {6, 1411}, {9, 80}, {19, 53}, {37, 101}, {44, 517}, {45, 55}, {57, 1020}, {63, 545}, {190, 321}, {198, 2164}, {484, 2245}, {654, 900}, {655, 673}, {909, 1319}, {910, 2222}, {1150, 12237}, {1400, 1989}, {1436, 2178}, {1635, 1769}, {1824, 2299}, {2259, 2264}

▸ Functional Relations7 relations

• X₂₁₆₁ = isogonal conjugate of X₃₂₁₈

• X₂₁₆₁ = X₂₀₀₆-Ceva conjugate of X₁₄₁₁

• X₂₁₆₁ = cevapoint of X_i and X_j for these (i,j): (37, 44), (649, 2087), (1635, 2170)

• X₂₁₆₁ = X_i-cross conjugate of X_j for these (i,j): (902, 1), (2183, 6)

• X₂₁₆₁ = crosspoint of X_i and X_j for these (i,j): (80, 2006), (88, 104)

• X₂₁₆₁ = crosssum of X_i and X_j for these (i,j): (36, 2323), (44, 517), (758, 2245)

• X₂₁₆₁ = trilinear pole of line X₄₂X₆₆₃