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SMO 2021 Junior Round 1 Question 4

SMO · SMO 2021 Junior Round 1

Question 4

In the diagram, six circles are tangent to each other. If the radius of the largest circle is $1$ and the radii of the four medium sized circles are equal, what is the radius of the smallest circle?

Question illustration
  1. $\sqrt2-1$
  2. $3-2\sqrt2$
  3. $2-\sqrt2$
  4. $6-4\sqrt2$
  5. None of the above