In the diagram, AB is a chord in the circle with centre O. C is the midpoint of AB. Click and drag any of the blue points to change the shape and orientation of the diagram. What observation can you make regarding the perpendicular bisector of the chord?
Using congruent triangles it is easy to prove that "a perpendicular to a chord from the centre of a circle bisects the chord". Given that there is only one perpendicular bisector of a chord, what does this tell you?