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# Pattern of Two Loci

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.

Cartesian Pattern

This entry contributed by Margherita Barile

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## References

Pólya, G. Mathematical Discovery: On Understanding, Learning, and Teaching Problem Solving, 2 vols. in One. New York: Wiley, 1981.

## Referenced on Wolfram|Alpha

Pattern of Two Loci

## Cite this as:

Barile, Margherita. "Pattern of Two Loci." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/PatternofTwoLoci.html