X₃₂₀₁

X₅₄-CEVA CONJUGATE OF X₁₆

X₃₂₀₁ = crosspoint of X₁₆ and X₆₁

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

X₃₂₀₁ (X₅₄-CEVA CONJUGATE OF X₁₆) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {17, 54}, {49, 61}

• Related Centers: X₅₄ (KOSNITA POINT), X₁₆ (2nd ISODYNAMIC POINT), X₁₇ (1st NAPOLEON POINT), X₄₉ (CENTER OF SINE-TRIPLE-ANGLE CIRCLE), X₆₁ (ISOGONAL CONJUGATE OF X₁₇)

Trilinears: \(u(-u/x + v/y + w/z) : v(u/x - v/y + w/z) : w(u/x + v/y - w/z)\), where \(x : y : z\) = X₅₄ and \(u : v : w\) = X₁₆

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): \(1.694700789901\)

▸ Alternate Coordinates2 forms

• Trilinears: \(\sin(A - \pi /3) \sin(2A - 2\pi /3) : \sin(B - \pi /3) \sin(2B - 2\pi /3) : \sin(C - \pi /3) \sin(2C - 2\pi /3)\) (M. Iliev, 4/12/07)

• Trilinears: \(\cos 3A + \cos(A - \pi /3) : \cos 3B + \cos(B - \pi /3) : \cos 3C + \cos(C - \pi /3)\) (M. Iliev, 4/12/07)

▸ Incident Central Lines9 lines

{3, 3206}, {6, 3200}, {14, 110}, {15, 184}, {17, 54}, {49, 61}, {62, 1147}, {203, 215}, {3104, 3202}

▸ Functional Relations3 relations

• X₃₂₀₁ = X_i-Ceva conjugate of X_j for these (i,j): (54, 16), (2981, 50)

• X₃₂₀₁ = crosspoint of X₁₆ and X₆₁

• X₃₂₀₁ = crosssum of X₁₄ and X₁₇