VMO 2000 Problem 1

Define a sequence of positive reals $x_0$, $x_1$, $x_2$, ... by $x_0$ = b, $x_{n+1}$ = √(c - √(c + $x_n$)). Find all values of c such that for all b in the interval (0, c), such a sequence exists and converges to a finite limit as n tends to infinity.