# Comparing Inside and the outside

Geometry Level 3

Above shows two figures. The one on the left shows a circumcircle and an incircle of an equilateral triangle. The ratio of their areas is 4.

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

$\lim_{n\to\infty} \frac{B_n}{A_n}$

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