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Synonyms for centroid are center of gravity and balance point, both of which indicate properties of this special point. The sketch here shows seven centroids associated with three disks.

If you drag point a away from point A, the other six centroids will "gravitate" toward A.

How could you arrange for point G to be the centroid of the triangle ABC?

How many triples of centroids in the sketch are collinear?

For more, see GEOMETRY IN ACTION, Chapter 2, Project 3.