Geometric algorithms for finding a point in the intersection of balls

We consider a problem of finding a point in the intersection of $n$ balls in the Euclidean space $E^m$. For the case $m=2$ we suggest two algorithms of the complexity $O(n^2\log n)$ and $O(n^3)$ operations, respectively. For the general case we suggest an exact polynomial recursive algorithm which uses the orthogonal transformation of the space $E^m$.