Three circles of the same radius

Given three circles with equal radii, there are several interesting ways to arrange them. The most common is to place them so that each pair of circles is tangent to each other (externally tangent). The centers of the circles then form an equilateral triangle with side length equal to twice the radius.

Important properties

• If three circles of the same radius are mutually externally tangent, the centers form an equilateral triangle.

• The distance between the centers of any two circles is twice the radius.

• The region enclosed between the three circles is called a 'Reuleaux triangle' if the circles are drawn around the triangle.

• If the circles are arranged differently, the centers may form other triangles, but the pairwise distance between centers is always at least twice the radius if the circles do not overlap.