# Comparing Inside and the outside

**Geometry**Level 3

The one on the right shows a circumcircle and an incircle of a unit square. The ratio of their areas is 2.

Now consider a \(n\)-sided regular polygon. Let the area of a circle inscribed in the regular polygon be \(A_n\). And let the area of a circle circumscribed the regular polygon with be \(B_n\). Evaluate

\[ \lim_{n\to\infty} \frac{B_n}{A_n} \]