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Australian AMC 2009 - Senior Question 19

AMC AUSTRALIA · Australian AMC 2009 - Senior

Question 19

In $\triangle PQT$, $PQ=10$ cm, $QT=5$ cm and $\angle PQT=60^\circ$. $PW,PY$ and $TQ$ are tangents to the circle with centre $S$ at $W,Y$ and $V$ respectively. The radius of the circle, in centimetres, is

Question illustration
  1. $\frac{5\sqrt3}{2+\sqrt3}$
  2. $\frac{5(3-\sqrt3)}2$
  3. $\frac5{1+\sqrt3}$
  4. $\frac{5\sqrt3}2$
  5. $\frac{25\sqrt3}6$