# How many circles to cover 2 times bigger circle?

How many circles (radius $r$) are needed to cover circle whose radius is $2$ times bigger (radius $2r$).

I think we need to use area which is $S=\pi R^2$ but I don't really know what to do.

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This is a difficult problem: First you have to devise a covering that you assume to be optimal. Then comes the difficult part: If your covering uses, say, 10 circles you have to prove that one definitely cannot do with 9 circles. The area estimate you propose could be an idea, but it only gives that you need at least 5 small circles: 4 for covering the area and at least one for the unavoidable overlap. – Christian Blatter Mar 8 '11 at 13:53
This page (www2.stetson.edu/~efriedma/circovcir) comes at it the other way: "How big a circle can I cover with n circles?". It claims the "I can cover a circle twice as big" case is trivial. – Rawling Mar 8 '11 at 14:19

The first task is to find the minimum number of small circles which cover the circumference of the bigger circle rather than the whole area. If this is $m$ then it will be impossible to have a regular $m$-gon with edges of length $2r$ fitting strictly inside the circle of radius $2r$. This implies $m \ge 6$.