If A B is a chord of the circle x 2 + y 2 = r 2 subtending a right angle at the centre. Then, the locus of the centroid of Δ P A B as P moves on the circle, is

Step-by-step solution

The given circle has the centre at the origin. Let P r cos θ , r sin θ and assuming A & B lie on the axes then their coordinates are r , 0   &   0 , r . If ( h , k ) is the centroid of the Δ P A B , then h = r ( 1 + cos θ ) 3 And k = r ( 1 + sin θ ) 3 ⇒ h - r 3 2 + k - r 3 2 = r 3 2 Hence, locus of h , k is x - r 3 2 + y - r 3 2 = r 3 2 which is a circle.