Let’s draw the diagram.
DIAGRAM
Minimum value of Angle $\text{AQP}$ is possible when, $\text{PQ = AP = AQ = r.}$ (When $\text{P}$ and $\text{Q}$ are at the intersection)
So, the triangle $\text{APQ}$ is an equilateral triangle.
Therefore each angle will be $60^{\circ}.$
If neither $\text{P}$ nor $\text{Q}$ full within the intersection of the circles.
Then $ < \text{AQP}<60^{\circ}.$
If we streach the circles then horizontal distance will be increases.
So, the value of $\text{AQP}$ will be decreased. So, $ < \text{AQP}>0^{\circ}.$
$\therefore \boxed{ 0^{\circ} < \text{AQP}<60^{\circ}}$
Correct Answer $:\text{C}$