a circle of constant radius r passes through the origin and meets the coordinate axes at point A and B respectively. Find the locus of the centroid of triangle OAB, O being the origin'
As AOB is a right angle so AB will be diameter of circle. If A is (h,o) then B is (0, sqrt(4r^2-h^2)). Centroid of this triangle is (h/3,sqrt(4r^2-h^2)/3). Put x =3h in y = sqrt(4r^2-h^2)/3 and we get x^2 +y^2 = 4r^2/9
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