Points of Concurrency
Each of these "centers" are the points of concurrency between different parts of the triangle. Determine which center is the point of concurrency between the three altitudes and medians of the triangle, the perpendicular bisectors of the three sides of the triangle, and the angle bisectors of the three angles in the triangle.
Are any of these "centers" ever outside the triangle? If so, which ones? What type of triangle has these centers outside? Move around the vertices to determine the answer to these questions.