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2011 AMC 10A Question 18

AMC10 · 2011 AMC 10A

Question 18

Circles $A,$ $B,$ and $C$ each have radius $1.$ Circles $A$ and $B$ share one point of tangency. Circle $C$ has a point of tangency with the midpoint of $\overline{AB}.$ What is the area inside circle $C$ but outside circle $A$ and circle $B?$

Question illustration
  1. $3 - \dfrac{\pi}{2}$
  2. $\dfrac{\pi}{2}$
  3. $2$
  4. $\dfrac{3\pi}{4}$
  5. $1+\dfrac{\pi}{2}$