Exploring Centers of Triangles
The applet below shows triangle ABT with four points of concurrency. A brief description of each point is listed to the right of the triangle. Follow the directions below the applet to make some discoveries.
Manipulate the vertices of triangle ABT to explore characteristics of the triangle's centers. Make conjectures based on, and provide visual evidence to support, the following leading questions: Are any of the centers collinear? Are the centers always within the interior of ABT? Do any of the centers delineate congruent or similar segments? How are the circumcenter and incenter situated "within" the triangle? Are they only centers for the triangle?