Mike May
This is a fast applet in an html page to give an example of posting
The three vertices of the triangle above can be dragged to show that the perpendicular bisectors of the three sides still meet in a single point when we look at other triangles. When a mathematician sees a behavior that works for all triangles (or at least with a bunch of examples that we have looked at) the suspicion is that there must be a structure that helps us prove in must always happen. The check box in the diagram provides the framework for the proof. Click the box "Show Circle" to see that any point on a bisector must be equally distant from two of the vertices. Any point on two bisectors must be equally distant from ll three vertices, so it must be on the third bisector.