In the sketch below, the circle has centre [math]O[/math] and radius [math]OR[/math]. The circle can be changed by moving either of these points.[br][br][math]A[/math] and [math]B[/math] are points on the circle, and can be moved on the circle. Construct the perpendicular bisector of the segment [math]AB[/math] and play around with it.
What special property(ies) does the perpendicular bisector of a chord of a circle have?