Discovering the Euler Line in a Triangle

Peg Fisher
Please follow the steps below to discover a unique line created from the three "remarkable" points of a triangle. 1. Construct an arbitrary triangle ABC using the polygon tool. 2. Use the custom tools found under the farthest right "tool" icon to create the circumcenter, orthocenter and centroid within triangle ABC.
Move the vertices of the triangle ABC and observe the relationship between the three "remarkable" points that you have constructed. Check your observation by entering the following in the Input bar: AreCollinear[<point>,<point>,<point>]