Two circles with centres \(A\) and \(B\), each with a radius of \(3\), are tangent to each other at \(S\). A straight line is drawn through \(A\), \(S\) and \(B\), meeting the circle with centre \(A\) at \(Q\), \(Q\neq S\), and the circle with centre \(B\) at \(R\), \(R\neq S\). Point \(P\) is then drawn so that \(PQ\) and \(PR\) are each tangent to the circle with centre \(A\).
Determine the length of \(PQ\).
Note: For this problem, you may want to use the following known results about circles:
If a line is tangent to a circle, then the line is perpendicular to the radius drawn to the point of tangency.
A line drawn from the centre of a circle perpendicular to a tangent line meets the tangent line at the point of tangency.
