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P is the variable point on the circle wi...

`P` is the variable point on the circle with center at `CdotC A` and `C B` are perpendiculars from `C` on the x- and the y-axis, respectively. Show that the locus of the centroid of triangle `P A B` is a circle with center at the centroid of triangle `C A B` and radius equal to the one-third of the radius of the given circle.

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