# What is the maximum number of circles in proximity to a given point.

The title maybe a bit obscure so I'll try my best to explain the problem here.

Below is the Picture that I'll take help from. Say I have a circle A of Radius R now if I take a point C inside this circle then obviously the center A will lie inside the circle originating from C with same radius R. Now I want to know, what is the maximum number of centers of circles(each of radius R) that can be there in the circle originating from C.

Instead of point C, no other center could be inside any other circle. To extend the example, if I have the circle with center B(Radius R), with center just outside the circle A, this center will also lie in the circle originating from C. Hence so long, I have the number to be Two, i.e. in circle from C, both centers A and B will lie.

So what is the maximum number?

## 1 Answer

If the centres are allowed to lie on the boundary of the other circles the answer is 6, if not, 5. To see this, take a regular hexagon and divide it into 6 equilateral triangles.