X₁₉₇₀

CROSSSUM OF PU(38)

X₁₉₇₀ = perspector of ABC and 1st Brocard triangle of orthic triangle

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

X₁₉₇₀ (CROSSSUM OF PU(38)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {3, 6}, {54, 112}

• Related Centers: X₃ (CIRCUMCENTER), X₆ (SYMMEDIAN POINT), X₅₄ (KOSNITA POINT), X₁₁₂ (Ψ(ORTHOCENTER, SYMMEDIAN POINT))

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = a(\sin^{2} 2A + \sin 2B \sin 2C)\)

Search Value (6, 9, 13): \(-0.295624468141\)

▸ Alternate Coordinates1 form

• Trilinears: \(\sin(A - \omega ') : :\), where ω’ = Brocard angle of orthic triangle

▸ Incident Central Lines3 lines

{3, 6}, {49, 1625}, {54, 112}

▸ Functional Relations1 relation

• X₁₉₇₀ = perspector of ABC and 1st Brocard triangle of orthic triangle