The applet below shows [color=#1551b5]triangle ABT[/color] 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[color=#1551b5] triangle ABT [/color]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 [i]interior[/i] of [color=#1551b5]ABT[/color]? Do any of the centers [i]delineate[/i] congruent or similar segments? How are the circumcenter and incenter situated "within" the triangle? Are they [i]only[/i] centers for the triangle?