The Euler Line
Leonhard Euler noticed that, in a triangle that is not equilateral, the Centroid, Circumcenter, and Orthocenter all lie on the same line.
Experiment with the triangle: select a vertex and move it around to make an acute, right, or obtuse triangle. Can you move the circumcenter and orthocenter outside the triangle? How about the centroid?
Can you make the three centers coincide? What kind of triangle do you need to make?
Check the Perpendicular Bisector box to show them in the triangle. Then try the altitudes and medians.