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1967 AMC 12 Question 33

AMC12 · 1967 AMC 12

Question 33

In this diagram semi-circles are constructed on diameters $AB,$ $AC,$ and $CB,$ so that they are mutually tangent. If $CD\perp AB,$ then the ratio of the shaded area to the area of a circle with $CD$ as radius is:

Question illustration
  1. $1:2$
  2. $1:3$
  3. $\sqrt3:7$
  4. $1:4$
  5. $\sqrt2:6$