Let AB be a chord of the circle  x2+y2=r2 subtending a right angle at the centre. Thus the locus of the centroid of the triangle PAB as P moves on the circle is

Let us take A≡(r,0) and B(0,r) subtending π2 angle at the centre Let P≡(rcosθ,rsinθ)So, G=r(1+cosθ)3,r(1+sinθ)3=(h,k) Step-IV: So, 3hr-12+3kr-12=1 which is a circle