Points on a Perpendicular Bisector of a Line Segment

In the applet below, the constructed perpendicular bisector of segment AB is shown. Add a point C on the perpendicular bisector. Join A to C and B to C to form a triangle ABC. Compare the lengths AC and BC . Move point C along the perpendicular bisector (anywhere above or below segment AB) Again check the lengths AC and BC . Make conclusions below.
What can you conclude about any point that lies on the perpendicular bisector of a segment? Hint: What did you notice about the purple point no matter where you put it?
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– Lew W. S., Tim Brzezinski

Information: Points on a Perpendicular Bisector of a Line Segment