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1971 AMC 12 Question 35

AMC12 · 1971 AMC 12

Question 35

Each circle in an infinite sequence with decreasing radii is tangent externally to the one following it and to both sides of a given right angle. The ratio of the area of the first circle to the sum of the areas of all the other circles in the sequence is:
  1. $(4+3\sqrt2):4$
  2. $9\sqrt2:2$
  3. $(16+12\sqrt2):1$
  4. $(2+2\sqrt2):1$
  5. $(3+2\sqrt2):1$