According to G. Pólya, the method of finding geometric objects by intersection.

1. For example, the centers of all circles tangent to a straight line at a given point lie on a line that passes through and is perpendicular to .

2. In addition, the circle centered at with radius is the locus of the centers of all circles of radius passing through .

The intersection of and consists of two points and which are the centers of two circles of radius tangent to at .

Many constructions with straightedge and compass are based on this method, as, for example, the construction of the center of a given circle by means of the perpendicular bisector theorem.