Manipulate the vertices of the triangle to investigate the location of the centers of a triangle.
1. Which two of the four centers are not always in the interior of the triangle?
2. What is true about the triangle when two of the centers are not inside the triangle?
3. When all four centers are in the interior of the triangle, which is closest to the largest angle?
4. Adjust the triangle above so that all four points of concurrency are located at the same point. What is true about triangle ABC when this happens?
5. Adjust this applet so that all of the points of concurrency are collinear on a horizontal line. What is true about the triangle in this situation? [i](hint: you will probably need to move more than one vertex)[/i]