The geometric centroid (center of mass) of the polygon vertices of a triangle is the point (sometimes also denoted ) that is also the intersection of the triangle's three triangle medians. The point is therefore sometimes called the median point. The centroid is always in the interior of the triangle (from Wolfram MathWorld).
R. A. Johnson, Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle, Boston, MA: Houghton Mifflin, 1929 p. 249.
D. Wells, The Penguin Dictionary of Curious and Interesting Geometry, London: Penguin, 1991 p. 150.