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2014 AMC 8 Question 20

AMC8 · 2014 AMC 8

Question 20

Rectangle $ABCD$ has sides $CD=3$ and $DA=5.$ A circle of radius $1$ is centered at $A,$ a circle of radius $2$ is centered at $B,$ and a circle of radius $3$ is centered at $C.$ Which of the following is closest to the area of the region inside the rectangle but outside all three circles?

Question illustration
  1. $ 3.5 $
  2. $ 4.0 $
  3. $ 4.5 $
  4. $ 5.0 $
  5. $ 5.5 $