Dart landing in the middle ring of a three-ring board

A dartboard is made of three concentric circles with radii $1$, $2$ and $3$ feet. A dart hits the board at a uniformly random point. Find the chance that the dart ends up in the middle ring, between radius $1$ and radius $2$.

$\tfrac13$. For a uniform point, probabilities are area ratios. The middle ring has area $4\pi-\pi=3\pi$ and the whole board has area $9\pi$, so the probability is $\tfrac{3\pi}{9\pi}=\tfrac13$.