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1952 AMC 12 Question 43

AMC12 · 1952 AMC 12

Question 43

The diameter of a circle is divided into $n$ equal parts. On each part a semicircle is constructed. As $n$ becomes very large, the sum of the lengths of the arcs of the semicircles approaches a length:
  1. Equal to the semi-circumference of the original
    circle
  2. Equal to the diameter of the original circle
  3. Greater than the diameter but less than the semi-circumference
    of the original circle
  4. That is infinite
  5. Greater than the semi-circumference but finite