Points of concurrency:

A few definitions to begin with:

orthocenter - the intersection of the three altitudes of a triangle.
centroid - the intersection of the three medians of a triangle. If a triangle could have constant area mass density, the centroid would be the center of mass, or balancing point.
circumcenter - the intersection of the perpendicular bisectors of the three sides of a triangle. The circumcenter is the center of the circumscribed circle.
incenter - the intersection of the bisectors of the three interior angles of a triangle. The incenter is the center of the inscribed circle.

Click below to investigate:

http://isite.lps.org/mjames2/resources/geogebra/geometry/c5_2_3_tri_four_points_conc.html