2025 AMC 12A Question 10 - thichhoctoan.com

Question 10

In the figure shown below, major arc $AD$ and minor arc $BC$ have the same center, $O.$ Also, $A$ lies between $O$ and $B,$ and $D$ lies between $O$ and $C.$ Major arc $AD,$ minor arc $BC,$ and each of the two segments $AB$ and $CD$ have length $2\pi.$

Question illustration

What is the distance from $O$ to $A?$

$1$
$1 - \pi + \sqrt{1 + \pi^2}$
$\dfrac{1}{2}\pi$
$\dfrac{1}{2}\sqrt{1 + \pi^2}$
$2$