how to solve it ???

I think that enough  for each circle-boundary to be
covered by others circles
or we have covering problem of arc by given set of arcs.

Have Ac based on this idea.

1504 ac with the same idea but
many hard work with eps.

Main difficult moment:
ends of arcs computed with help of arcos
have error with respect to exact values and may be
greater or smaller of them , but exact values of boundaries of intervals lies in distance eps=1.e-16 from computed values.


Edited by author 22.03.2008 17:50

It's Vorony diagrams problem. Of course, you may solve it via covering all arcs of all circles or even try binary search on radius.

2svr: as for comparing arcs - why do you need angles? Just keep x/y pairs defining direction and compare these pairs for <, =, > of angles they define. One of easy easy ways to do that:
y>0 || y==0 && x>0 - 1st part [0;pi)
y<0 || y==0 && x<0 - 2nd part [pi;2pi)

if 2 vectors belong to different parts, you alredy know which angle is smaller. If not, check sign of their cross product.