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SMO 2013 Senior Round 1 Question 8

SMO · SMO 2013 Senior Round 1

Question 8

A square $ABCD$ and an equilateral triangle $PQR$ are inscribed in a circle centred at $O$ in such a way that $AB\parallel QR$. The sides $PQ$ and $PR$ of the triangle meet the side $AB$ of the square at $X$ and $Y$ respectively. The value of $\tan\angle XOY$ is

Question illustration
  1. $\frac1{\sqrt3}$
  2. $1$
  3. $\frac{\sqrt6-\sqrt3}{\sqrt2}$
  4. $\frac{2\sqrt2-2}{\sqrt3}$
  5. $\sqrt3$