Challenge 39: The Centroid of a Triangle
- Gerry Stahl
There are a number of interesting ways to define the “center” of a triangle, each with its own special properties. The “centroid” of a triangle is the meeting point of the three lines from the midpoints of the triangle’s sides to the opposite vertex. The centroid is the triangle’s “center of gravity.” (If you made a cardboard triangle, it would balance on the centroid.) If you are using a version of GeoGebra that allows you to create custom tools, then create your own tool for constructing a centroid of a triangle. Also, create your own tools for the circumcenter, orthocenter and incenter of a triangle and use these custom tools to construct the Euler segment and the nine-point circle.