(a) Let $A_n$ be the area of a polygon with $n$ equal sides inscribed in a circle with radius $r$. By dividing the polygon into $n$ congruent triangles with central angle $2\pi/n,$ determine which of the following is a correct expression for $A_n:$

A. $\displaystyle \frac{1}{2}nr^2\sin\left(\frac{\pi}{n}\right)$
B. $\displaystyle nr^2\sin\left(\frac{2\pi}{n}\right)$
C. $\displaystyle \frac{1}{2}n^2r\sin\left(\frac{2\pi}{n}\right)$
D. $\displaystyle \frac{1}{2}nr^2\sin\left(\frac{2\pi}{n}\right)$

(b) Compute the limit as $n$ goes to infinity of the correct answer to (a). Value of limit =