A circle is centered at $O.$ The tangent to the circle at $P$ is extended to $Q.$ Line segment $\overline{QS}$ intersects the circle at $R.$ Given that $OS = 2,$ $SR = RQ = 3$, and $PQ = 6$, find the radius of the circle.
[asy] unitsize(2 cm); pair A, B, C, D, E, F, G, O; A = dir(70); B = A + 1.2*dir(-20); C = dir(25); D = 2*C - B; O = (0,0); draw(Circle(O,1)); draw(A--B--D--O); dot("$P$", A, N); dot("$Q$", B, dir(0)); dot("$R$", C, SW); dot("$S$", D, NW); dot("$O$", O, SW); [/asy]
