2006 AMC 10B Question 19 - thichhoctoan.com

Question 19

A circle of radius $2$ is centered at $O.$ Square $OABC$ has side length $1.$ Sides $\overline{AB}$ and $\overline{CB}$ are extended past $B$ to meet the circle at $D$ and $E,$ respectively. What is the area of the shaded region in the figure, which is bounded by $\overline{BD},$ $\overline{BE},$ and the minor arc connecting $D$ and $E?$

Question illustration

$\dfrac{\pi}{3}+1-\sqrt{3}$
$\dfrac{\pi}{2}(2-\sqrt{3})$
$\pi(2-\sqrt{3})$
$\dfrac{\pi}{6}+\dfrac{\sqrt{3}-1}{2}$
$\dfrac{\pi}{3}-1+\sqrt{3}$