Let a circle of radius 4 pass through the origin O, the points A (-√ 3 a, 0) and B (0,-√ 2 b), where a and b are real parameters and a b ≠ 0. Then…

Let a circle of radius $\displaystyle 4$ pass through the origin O , the points $\displaystyle \mathrm{A}(-\sqrt{3} a, 0)$ and $\displaystyle \mathrm{B}(0,-\sqrt{2} b)$, where $\displaystyle a$ and $\displaystyle b$ are real parameters and $\displaystyle a b \neq 0$. Then the locus of the centroid of $\displaystyle \triangle \mathrm{OAB}$ is a circle of radius