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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.
