The figure at right shows two concentric circles.  

1. Which arc has greater measure: $\overarc{ A B }$ and $\overarc{ C D }$? Explain.

   Answer (a):

   They are similar. Both are the intercepted arc of central angle $∠CPD$.

2. Which arc has greater length? Explain how you know.

   Hint (b):

   We already know that both share the same central angle. Which one has a larger radius?

   Answer (b):

   Both arcs have the same measure.

   $\overarc{CD}$ has greater length.

3. If $m∠P = 60°$ and $PD=14$, find the length of $\overarc{ C D }$. Show all work.

   Step 1(c):

   Arc $\overarc{CD}$ is a fraction of a circle with a radius of $14$ and a circumference of $2πr = 2π(14) = 28π$.

   Step 2(c):

   Therefore, the length of $\overarc{CD} = \frac{60}{360} (28\pi)$.