# The smallest disc which could contain 11 coins

There are $11$ coins with $1$ unit radius and we are trying to put them inside a big disc with some radius. So

What is the minimum radius of this disc?

• If this question was asked for $2$ coins, the answer would be obviously $2$ unit radius,
• If was asked for $3$ coins, the answer would be $1+\frac{2}{\sqrt{3}}\cong 2.16$ unit radius as shown below:

$1+\frac{1}{\sin\frac{\pi}{9}}\approx3.923$