Given a segment AB, Determine and build the locus of points equidistant from points A and B.

The set of points removed from point A by the same distance R forms a circle of radius R centered at point A. Similarly, points removed by the same distance R form another circle with radius R centered at point B. If R is more than half of the segment AB, then they intersect at two points – K and L. If we connect these points, then we get the segment KL, perpendicular to the segment AB, dividing AB in half (property of the rhombus diagonals). These constructions are valid for any radius R> AB / 2, from which it follows that the locus of points equidistant from points A and B is a straight line perpendicular to the segment AB and dividing it in half.