Smallest range of angle between intersecting circles

In $\triangle APQ$, $AP = AQ = r$. So $\triangle APQ$ is isosceles. Since P and Q lie outside the intersection, the distance $PQ$ ranges between $r$ and $2r$. When $PQ = r$, $\triangle APQ$ is equilateral and $\angle AQP = 60^\circ$. As $PQ \to 2r$, $\angle AQP \to 0^\circ$. So angle AQP ranges between $0^\circ$ and $60^\circ$.