Move C &/or D to adjust the segment. Place the centers of the two congruent circles on points C & D.[br]Increase the radius slider until the circles intersect. Locate the points of intersection of the circles. [br]Draw a line through the points of intersection. This new line intersects the segment at the mid-point and is [br]perpendicular to the segment.

Construct the perpendicular bisector using the congruent circles.