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2010 AMC 8 Question 19

AMC8 · 2010 AMC 8

Question 19

The two circles pictured have the same center $C.$ Chord $\overline{AD}$ is tangent to the inner circle at $B,$ $AC$ is $10,$ and chord $\overline{AD}$ has length $16.$ What is the area between the two circles?

Question illustration
  1. $ \ 36 \pi $
  2. $ \ 49 \pi $
  3. $ \ 64 \pi $
  4. $ \ 81 \pi $
  5. $ \ 100 \pi $