$P$ is the variable point on the circle with center at $C \dot{C} A$ 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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Charlotte Discussed

P

is the variable point on the circle with center at

C \dot{C} 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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