Equidistant

Points equidistant from two fixed points lie on the perpendicular bisector of the segment joining them. Within a given angle, points equidistant from its two sides lie on its angle bisector; distance to each side is measured perpendicularly. Construct the relevant lines or circles first, then look for their intersections or overlapping regions.

Every point on an angle bisector is equidistant from the two arms of the angle, where distance from a point to a line is measured perpendicularly. Conversely, a point inside an angle that is equidistant from its arms lies on the angle bisector. This is why an angle bisector can also represent a locus, although the construction here is simply the required ruler-and-compass method.