If you drop only 50 points, you'll not detect many little "white spaces" (when, for example, current radius 1e-3 less, than optimal. Obviously, such a solution will get WA.
How to check coverage with bruteforce? Intersect any two circles and consider epsilon neighborhood of their common points...

Thanks a lot. But perhaps if I increase the number of random points (for each check a separate set of points), I'll get AC (if not from the first time, than from the second thanks to the random :)

To my mind, it's practically impossible. You should check (1000/1e-5)^2 ~ 10^16 points on every step of binsearch to catch "little whitespaces". Quadrotrees can help you a little, but...

Your idea is very good, but how you did it so fast?
I have TL16

theriyaathutaa koothi

Apply some optimixation techniques - precalc, for instance...

Now I have WA17
I do not understand what points should we check
If we will check only neighboor points of
intersection any 2 circles - it's not right

For example
2 1000
1000 0
999 0

Right answer is 1999

But if we will check radius 1000 then both intersection points will lie out of main circle

For each two crossing circles (crossing inside main circle) there must be third one which covers intersection point of the first two circles.

can you tell me more about your solution

how can you solve this problem without the diagram

I don't understand you solution
tell me more