This page is full of links to Geometer's Sketchpad (GSP) scripts, which allows you to repeat constructions that are done in GSP without having to repeat all the steps of getting there.
To create the different geometric figures or properties, click on the arrow in the toolbox and select the thing that you would like to create. Then, just begin drawing, and it will automatically create whatever you have chosen.
By clicking on "Triangle Tools" below, you will be taken to a document in GSP which will allow you to create the following properties for triangles:
Centroid
Orthocenter
Circumcenter
Circumcirle
Incenter
Incircle
Euler line
For the Euler line, the centroid will always be the point between the orthocenter and circumcenter. The circumcenter will be equidistant from all three vertices, and the distance from the circumcenter to the centroid will be one-third the distance from the circumcenter to the orthocenter.
Here are some links to other scripts:
Creating an Equilateral Triangle
Create a Square Given One Side