I have a question which asks me to work with centroids for a triangle. basically i need to determine (as a function of the angle or side) what masses to place on the vertices of an triangle so that the median coincides with the orthocenter and circumcenter.

i was given this to work with:

The centroid, G of a set of points is defined vectorially by:

Code:
                              -->
              -->   Sum(m_i * OM_i)
              OG =---------------------       
                      Sum(m_i)
which looks very similar to a formula of weighted means. but i have never worked with vectors before. anyone care to give me an example?