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SMO 2026 Junior Round 1 Question 2

SMO · SMO 2026 Junior Round 1

Question 2

In the diagram below, five circles are arranged so that each inner circle is tangent to its adjacent inner circles and to the largest circle. The vertices of the shaded quadrilateral are the centres of the four circles inside the largest circle. If the diameter of the largest circle is $x$ cm, what is the area of the shaded quadrilateral in $\mathrm{cm}^2$ in terms of $x$?

Question illustration
  1. $\frac{x^2}{12}$
  2. $\frac{x^2}{6}$
  3. $\frac{x^2}{4}$
  4. $\frac{x^2}{3}$
  5. $\frac{x^2}{2}$