Q. Let AB be 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 the $\Delta PAB$ as P moves on the circle, is

Solution:

Choosing OA as X-axis, A = (r,0), B = (0, r) and any point P on the circle is (r $cos\theta$, r $sin\theta$). If (x, y) is the centroid of $\Delta$ PAB, then 3x=r $cos\theta$ + r + 0 and 3y=r $sin \theta$ + 0 + r $\therefore$ $(3x - r)^2 + (3y - r)^2 = r^2$ Hence, locus of P is a circle.

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