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3.02 Construct the Perpendicular Bisector of a Segment

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

What is required of the radius size in order to construct the perpendicular bisector?