LocusMedium

Locus of Triangle Centroid

Let ⁿC_r–1 = 28, ⁿC_r = 56 and ⁿC_r+1 = 70. Let A(4cost, 4sint), B(2sint, –2cost) and C(3r – n, r²– n – 1) be the vertices of a triangle ABC, where t is a parameter. If (3x – 1)² + (3y)² = α, is the locus of the centroid of triangle ABC, then α equals :

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