You might use Helly's Theorem: $n \ge 3$ convex sets in the plane have a common intersection if and only if every three of the sets intersects.
There are faster algorithms:
Aurenhammer, Franz. "Improved algorithms for discs and balls using power diagrams." Journal of Algorithms 9, no. 2 (1988): 151-161. DOI.
Later edit. I found this nice figure in answer to an MSE question, the intersection of n disks/circles:
You might use Helly's Theorem: $n \ge 3$ convex sets in the plane have a common intersection if and only if every three of the sets intersects.
There are faster algorithms:
Aurenhammer, Franz. "Improved algorithms for discs and balls using power diagrams." Journal of Algorithms 9, no. 2 (1988): 151-161. DOI.
You might use Helly's Theorem: $n \ge 3$ convex sets in the plane have a common intersection if and only if every three of the sets intersects.
There are faster algorithms:
Aurenhammer, Franz. "Improved algorithms for discs and balls using power diagrams." Journal of Algorithms 9, no. 2 (1988): 151-161. DOI.
Later edit. I found this nice figure in answer to an MSE question, the intersection of n disks/circles:
