You all know what a perpendicular bisector is: the locus of points equidistant from two given points. We can go further and consider loci of points equidistant not from individual points, but from other sets of points. Generalizing the idea, we can then ask: what is the locus of points equidistant from a point and a line? From a point and a circle? From a line and a circle? More ambitiously still, we might imagine the locus of points equidistant from two circles or even—let's go wild!—from a line and a square. So many loci to determine before we explore them!
Points, lines and circles
---------------------------------------
The circle is the simplest such locus: it is the locus of points equidistant from its center. Another very simple example is the angle bisector of a pair of intersecting lines: it is nothing other than the locus of points equidistant from the two lines.
