Intersecting circles

Given two circles in a plane, they can intersect in zero, one, or two points. The number of intersection points depends on the distance between their centers and their radii.

Important properties

• If the distance between centers is greater than the sum of the radii, the circles do not intersect.

• If the distance between centers equals the sum or the difference of the radii, the circles are tangent (touch at one point).

• If the distance between centers is less than the sum but greater than the absolute difference of the radii, the circles intersect at two points.

• The line joining the intersection points is called the common chord.