# A Special Theorem: Part 1 (V1)

- Author:
- Tim Brzezinski

In the applet below, note that point

*C*is equidistant from*A*and*B*. In this applet,**Also note that***C*will ALWAYS REMAIN EQUIDISTANT from*A*and*B*.*A*and*B*serve as endpoints of a segment.**Directions:**1) Drag*C*around as much as you'd like (without moving*A*and*B*). What can you conclude about the locus (set of points) in the plane that are equidistant from the endpoints of a segment? What does this locus look like? 2) Let's test this conjecture again. Change the location of point*A*and point*B*. Hit the "Clear Trace" button to erase the previous traces of point*C*. Repeat Step 1. 3) Use the tools of GeoGebra to now show that your conjecture is true.