[b]Euler line[/b] of a triangle is the straight line that contains the [i]circumcenter[/i], the [i]centroid[/i], and the [i]orthocenter[/i] of the triangle. [br][br]Recall... [i]circumcenter[/i] is the point of concurrency of the perpendicular bisectors of a triangle;[br] [i]centroid[/i] is the point of concurrency of the medians of a triangle;[br] [i]orthocenter[/i] is the point of concurrency of the altitudes in a triangle.[br][br]The applet below shows the [b]Euler line[/b] of triangle [i]ABC[/i] that contains its [i]centroid, G[/i], [i]circumcenter, J[/i], and [i]orthocenter, I[/i]. [br]Drag any of the vertices of triangle [i]ABC[/i] and observe the movement of these points, [i]G, J[/i], and [i]I[/i], in relation to the corresponding change in the triangle. [br]In addition, compare the distances from the centroid to the orthocenter and from the centroid to the circumcenter.