Many real-life problems can be considered from the point of view of centroids, circumcenters, orthocenters, and incenters of triangles. Here are three activities to try:

Download this free article from the National Council of Teachers of Mathematics to figure out the best place for three friends to meet for lunch.

Click here to consider the best location for an airport that serves three cities. 

Here is a hospital locator activity from NCTM Illuminations.