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Australian AMC 2010 - Intermediate Question 17

AMC AUSTRALIA · Australian AMC 2010 - Intermediate

Question 17

Two squares are drawn inside a circle with centre $O$. The larger square touches the circle at each of its corners. The smaller square touches the circle at two of its corners and one of its sides passes through the centre of the circle as shown.

What is the ratio of the area of the larger square to that of the smaller square?

Question illustration

**Source annotation note:** Faint handwritten marks in the supplied image are preserved for fidelity. They are not printed givens or an official answer.
  1. $3:1$
  2. $5:2$
  3. $\sqrt5:2$
  4. $2:1$
  5. $3:\sqrt6$