Euler's Discover

Task 1 -Open a new GeoGebra window and import your three custom tools (circumcenter.ggt, orthocenter.ggt and centroid.ggt) into the Toolbar.  Create an arbitrary triangle ABC and apply all three custom tools to the triangle in order to create the circumcenter, orthocenter and centroid within the same triangle. -Move the vertices of triangle ABC and observe the three ‘remarkable’ points you just constructed. Which relationship do they have? Use one of GeoGebra’s geometry tools in order to visualize this relationship.
It seems as though an equilateral triangle (all angles being 60 degrees) results in the orthocenter, circumcenter, and centroid laying at the same point. If we were to inscribe the triangle inside of a circle, this point would be the center of the circle. This means that this point is the balancing point of the triangle.