If a circle of constant radius `3c` passes through the origin and meets the axes at `A and B` , prove that the locus of the centroid of ` triangleA B C` is a circle of radius `2c`

Explanation

Let the coordinates of A and B are (a,0) and (0,b) respectively


Clearly, OAB is a right-angled triangle, the hypotenuse AB is a diameter of the circle.


Thus AB=2(3k)=6k


In traingle AOB,


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