Centers of a Triangle

We have talked a little about the centers of a triangle. Move the vertices of triangle ABC to investigate the placement of each of the centers.

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1. How are each of the centers of triangle ABC found?
2. Do all the centers need to be inside the triangle? If not, which one(s) do not?
3. Is it possible for all the centers to occur at the same point? If so, use the tools to figure out the properties of the triangle when this happens.

Mindy Burcham, Created with GeoGebra