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1966 AMC 12 Question 31

AMC12 · 1966 AMC 12

Question 31

Triangle $ABC$ is inscribed in a circle with center $O'.$ A circle with center $O$ is inscribed in triangle $ABC.$ $AO$ is drawn, and extended to intersect the larger circle in $D.$ Then we must have:

Question illustration
  1. $CD=BD=O'D$
  2. $AO=CO=OD$
  3. $CD=CO=BD$
  4. $CD=OD=BD$
  5. $O'B=O'C=OD$