I agree with S = 1. Here is my approach.
OP and OQ are the radii of the circle. From OP, we can find the radius = 2 (aplying distance between two points formula)
OP = OQ ie applying distance forumal between OQ will give s^2 + t^2 = 4 ---eq 1.
In triangle POQ, <O = 90 and two sides are equal. By 45:45:90 rules, sides will be 1;1:sqrt 2. So the distance between PQ = 2 sqrt 2.
Now apply distance forumal for PQ equating it to 2 (sqrt 2) we get sqrt(3)*s = t. ----Eq 2
Substituting eq 2 in eq 1, we get s = 1.
I doubt this problem can be solved with in 2 min when we look at the problem for the firs time. I almost took 6 min and trying since I know I can solve but definitely not with in 2 min. Good to know some other alternate approaches as well.