three symmetrically placed equal circles

Question

If three symmetrically placed equal circles intersect in a single point, as illustrated in the figure. What should be the distance between the centre of the three circle for obtaining such a overlap.

Answer 1

Simple geometry:

radius $r=OA=OB=OC=OD=OE=OF$ and $AB=BC=CA=r\sqrt{3}$

Answer 2

It is a very easy question. $AB=BC=CA=r\sqrt 3$ where $A,B,C$ are the centers of the circles and $r$ is the radius of the circles.